21. Sun-Yung Alice Chang Director of Graduate Studies, Department of Mathematics, Princeton University. Subjects geometric analysis, algebraic geometry, differential geometry. http://www.math.princeton.edu/~chang/

Sun-Yung Alice Chang Department of Mathematics, Princeton University email: chang@math.princeton.edu Office Phone: 609-258-5114 MathSciNet Home Page Recent preprints (Differential Geometry) Recent preprints (Analysis of PDE New Papers Sun-Yung A. Chang , Jie Qing and Paul Yang, ``On finiteness of Kleinian groups in general dimension," preprint 2002, to appear in the Crelles Journal.[ pdf] Sun-Yung A. Chang, C.C. Chen aand C. S. Lin, ``Extremal functions for a mean field equation in two dimension,'' Lecture on Partial Differential equations in honor of Louis Nirenberg's 75th birthday, Chapter 4, International Press, 2003.[ pdf] Sun-Yung A. Chang, Matt Gursky and Paul Yang ``Entire solutions of a fully non-linear equation,'' Lecture on Partial Differential Equations in honor of Louis Nirenberg's 75th birthday, Chapter 3, International Press, 2003.[ pdf Sun-Yung A. Chang , Matt Gursky and Paul Yang , ``A conformally invariant sphere theorem in four dimensions'', to appear Publications de l'IHES, 2003. [ pdf Sun-Yung A. Chang and Paul Yang, ``Non-linear Partial Differential equations in Conformal Geometry", Proceedings for ICM 2002, Beijing, volume I, pp 189-209.[

22. Natural Operations In Differential Geometry Natural operations in differential geometry. First it should be a monographical work on natural bundles and natural operators in differential geometry. http://www.emis.de/monographs/KSM/

The Electronic Library of Mathematics Mathematical Monographs For fastest access: Choose your nearest mirror site! Natural operations in differential geometry by Ivan Kolar, Jan Slovak and Peter W. Michor Paper version originally published by Springer-Verlag, Berlin, Heidelberg, New York, 1993 ISBN 3-540-56235-4 (Germany) Download the whole book as one file: HYPER-DVI ] (838,207 bytes) Postscript ] (1,330,587 bytes) PDF ] (2,945,143 bytes) The aim of this book is threefold: First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. Even though Ehresmann in his original papers from 1951 underlined the conceptual meaning of the notion of an $r$-jet for differential geometry, jets have been mostly used as a purely technical tool in certain problems in the theory of systems of partial differential equations, in singularity theory, in variational calculus and in higher order mechanics. But the theory of natural bundles and natural operators clarifies once again that jets are one of the fundamental concepts in differential geometry, so that a thorough treatment of their basic properties plays an important role in this book. We also demonstrate that the central concepts from the theory of connections can very conveniently be formulated in terms of jets, and that this formulation gives a very clear and geometric picture of their properties.

23. Geometry/Topology Page GEOMETRY and TOPOLOGY. differential geometry + Differential Forms Noncommutative and Quantum Geometry + Topology and Topological Field Theory. differential geometry http://web.mit.edu/afs/athena.mit.edu/user/r/e/redingtn/www/netadv/diffgeom.html

The Net Advance of Physics: GEOMETRY and TOPOLOGY Differential Geometry Differential Forms Geometric Probability Noncommutative and Quantum Geometry ... Topology and Topological Field Theory DIFFERENTIAL GEOMETRY: General and Various: Self-Avoiding Random Manifolds, by Francois David, 95/11 Quantum Theory of Large Systems of Non-Relativistic Matter, by J. Froehlich, U.M. Studer and E. Thiran, 95/08 Riemann Surfaces, (Chapter 5 of "Two Dimensional QCD is a String Theory", thesis by Soeren Koester), 94/08 page 52. Introduction to Duality, by Amit Giveon and Martin Rocek, 94/06 Non-Commutative Geometry Cartan Differential Forms: Bill Burke's Differential Forms Page Riemannian Geometry: General: The Net Advance of Physics: GENERAL RELATIVITY Torsion: Quantum Theory of Large Systems of Non-Relativistic Matter, by J. Froehlich, et al., 95/08: (page 12) The Net Advance of Physics: DISLOCATIONS The Net Advance of Physics: GENERAL RELATIVITY Spinors: Introduction to Division Algebras, Sphere Algebras, and Twistors, by Martin Cederwall, 93/10: The Net Advance of Physics: SPINORS INTEGRAL GEOMETRY AND GEOMETRIC PROBABILITY: Minkowski Functionals in Cosmology, by J. Schmalzing et al., 95/08

24. EMIS ELibEMS: Mathematical Conference Proceedings Proceedings of the. 5th International Conference on. differential geometry and Its Applications. Opava, Czechoslovakia August 2428, 1992. Editors. http://www.emis.de/proceedings/5ICDGA/

The Electronic Library of Mathematics Mathematical Conference Proceedings Proceedings of the 5th International Conference on Differential Geometry and Its Applications Opava, Czechoslovakia August 24-28, 1992 Editors O. Kowalski and D. Krupka For fastest access: Choose your nearest server! Contents (Point to Abs to get an abstract, point to DVI to get a DVI file, point to PS to get a PostScript file, point to Add to get an addendum.) Preface Part I. Analysis and Topology on Manifolds S. Armas-Gomez, J. Margalef-Roig, E. Outerelo-Dominguez, E. Padron-Fernandez, Openess and density theorems of transversality in manifolds with corners Abs DVI PS X. Gual Arnau, Abs DVI PS Add S. Helgason, The Fourier transform on symmetric spaces and applications Abs DVI PS P. Libermann, On symplectic and contact groupoids Abs DVI PS A. Tralle, On compact homogenous spaces with non-vanishing Massey products Abs DVI PS Tran Quyet Thang, Cousin problem for monogenic functions with parameter in Clifford analysis Abs (Full text not available in electronic form) Part II. Differential Equations on Manifolds

25. Ricci: A Mathematica Package For Doing Tensor Calculations In Differential Geome A Mathematica package for doing tensor calculations in differential geometry and general relativity. http://www.math.washington.edu/~lee/Ricci/

Ricci A Mathematica package for doing tensor calculations in differential geometry Version 1.37 Last Updated November 12, 2002 Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It has the following features and capabilities: Manipulation of tensor expressions with and without indices Implicit use of the Einstein summation convention Correct manipulation of dummy indices Display of results in mathematical notation, with upper and lower indices Automatic calculation of covariant derivatives Automatic application of tensor symmetries Riemannian metrics and curvatures Differential forms Any number of vector bundles with user-defined characteristics Names of indices indicate which bundles they refer to Complex bundles and tensors Conjugation indicated by barred indices Connections with and without torsion Limitations: Ricci currently does not support computation of explicit values for tensor components in coordinates, or derivatives of tensors depending on parameters (as in geometric evolution equations or calculus of variations), although support for these is planned for a future release. Ricci also has no explicit support for general relativity, or for other mathematical physics or engineering applications, and none is planned. If you are interested in such support, I recommend that you consider the commercial package MathTensor, which is far more extensive than Ricci, and provides all these capabilities and more. MathTensor is available from

26. Journal Of Differential Geometry Journal of differential geometry. The Journal of differential geometry is published at Lehigh University. Call 610758-3750 to speak http://www.lehigh.edu/~math/jdg.html

Journal of Differential Geometry The Journal of Differential Geometry is published at Lehigh University. Call 610-758-3750 to speak to editor-in-chief Professor C.C. Hsiung or call 610-758-3726 to speak to the managing editor Professor Huai-Dong Cao Some photos of the May 1996 conference at Harvard University celebrating the 30th anniversary of the journal and the 80th birthday of its founder, C.C. Hsiung, emeritus professor in the Lehigh University Department of Mathematics. JDG sponsors the annual Lehigh University Geometry/Topology Conference. JDG information People involved in JDG Submissions ... Journal of Differential Geometry Online (International Press) Journal of Differential Geometry Online (Project Euclid)

27. Geometry Formulas And Facts An excerpt from the 30th Edition of the CRC Standard Mathematical Tables and Formulas, covering the area of Geometry (minus differential geometry), by Silvio Levy. http://geom.math.uiuc.edu/docs/reference/CRC-formulas/

Next: Part I: Two-Dimensional Geometry Up: Geometry Reference Archives Geometry Formulas and Facts Silvio Levy This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas , published in late 1995 by CRC press This completely rewritten and updated edition of CRC's classical reference work is edited by Dan Zwillinger, and boasts the participation of dozens of distinguished contributors in all fields of mathematics. Ordering information is available here The present excerpt covers the area of Geometry (minus differential geometry). It was written by Silvio Levy and is reproduced here with permission. All the figures were made by the author using Mathematica , except those in Section , which were made using kali This online version was prepared with the help of Nikos Drakos's converter; for compatibility of text and formulas, choose a largish text font with your browser. A button in the text indicates a cross-reference. Part I: Two-Dimensional Geometry 1 Coordinate Systems in the Plane 1.1 Substitutions and Transformations 1.2 Cartesian Coordinates in the Plane ... 16 Quadrics Next: Part I: Two-Dimensional Geometry Up: Geometry Reference Archives The Geometry Center Home Page Silvio Levy Wed Oct 4 16:41:25 PDT 1995 This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas CRC Press ). Unauthorized duplication is forbidden.

28. Workshop On Differential Geometry Workshop on differential geometry. Dates Monday 25th March Wednesday 27th March 2002. Location Coffee Breaks will be held in http://www.maths.adelaide.edu.au/groups/iga/wdg.html

Workshop on Differential Geometry Dates : Monday 25th March - Wednesday 27th March 2002. Location : Coffee Breaks will be held in Engineering and Mathematics Building, Room EM117. Lectures will be held in various locations. Coffee and Tea will be available from about 9am every day in EM117. Here is a map of campus. Organiser : Michael Eastwood (meastwoo@maths.adelaide.edu.au). There is no registration fee. All interested are welcome. Speakers Alan Carey (Australian National University) Michael Cowling (University of New South Wales) Tony Dooley (University of New South Wales) Michael Eastwood (Adelaide University) Klaus Ecker (Monash University) Min-Chun Hong (Australian National University) Gen Komatsu (Osaka University) Michael Murray (Adelaide University) Hyam Rubinstein (University of Melbourne) Paul Tod (University of Oxford) Neil Trudinger (Australian National University) Joseph Wolf (University of California at Berkeley) Programme The workshop will start on Monday at 10:15am and finish on Wednesday at 4:30pm. The programme is available here Titles and Abstracts They can be found here Funding There will be some financial support available to interstate participants, with graduate students being given priority.

29. GRAPE - Graphics Programming Environment A package for mathematical visualization, particularly in the fields of differential geometry and continuum mechanics. Available free by FTP but only to university departments and similiar research sites and only for nonprofit purposes. http://www-sfb256.iam.uni-bonn.de/grape/

GRAPE - Graphics Programming Environment Welcome to the GRAPE information pages. GRAPE is a package for mathematical visualization. It has been particularly effective in the fields of differential geometry and continuum mechanics. But it will probably help to understand any other problem involving the numerics of partial differential equations or the need of advanced three-dimensional computer graphics. GRAPE is developed and distributed by the Sonderforschungsbereich 256 "Nichtlineare Partielle Differentialgleichungen" 53115 Bonn Germany in cooperation with the at the University of Freiburg Please feel free to use any of the services offered. If there is any information you still need, please don't hesitate to send us e-mail (see bottom of page for address). Short Introduction to GRAPE Get a GRAPE License Download Package and Manuals Information (last update: March 13, 1997) GRAPE 5.3 Manual (access for local users only) HMesh Manual (access for local users only) News: Bonn Freiburg (access for local users only) Bugs: Bonn (access for local users only) As part of the software development is done at the , we strongly recommend that you take a look at their World Wide Web server ( GRAPE in Freiburg ), too.

30. DC MetaData For: Natural Operations In Differential Geometry Ivan Kolar, Jan Slovak, Peter W. Michor Natural operations in differential geometry The book is published SpringerVerlag, Berlin, Heidelberg, New York, 1993 http://www.mat.univie.ac.at/~michor/preprint-shadows/kmsbookh.html

Ivan Kolar, Jan Slovak, Peter W. Michor Natural operations in differential geometry The book is published: Springer-Verlag, Berlin, Heidelberg, New York, 1993 MSC 53-02 Research exposition (monographs, survey articles) 53-01 Instructional exposition (textbooks, tutorial papers, etc.) 58-02 Research exposition (monographs, survey articles) 58-01 Instructional exposition (textbooks, tutorial papers, etc.) 53A55 Differential invariants (local theory), geometric objects 53C05 Connections, general theory 58A20 Jets Abstract The aim of this book is threefold: First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. Even though Ehresmann in his original papers from 1951 underlined the conceptual meaning of the notion of an $r$-jet for differential geometry, jets have been mostly used as a purely technical tool in certain problems in the theory of systems of partial differential equations, in singularity theory, in variational calculus and in higher order mechanics. But the theory of natural bundles and natural operators clarifies once again that jets are one of the fundamental concepts in differential geometry, so that a thorough treatment of their basic properties plays an important role in this book. We also demonstrate that the central concepts from the theory of connections can very conveniently be formulated in terms of jets, and that this formulation gives a very clear and geometric picture of their properties.

31. Prof. C.B. Thomas University of Cambridge. Application of algebraic topology to differential geometry. http://www.dpmms.cam.ac.uk/site2002/People/thomas_cb.html

Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. C.B. Thomas Prof. C.B. Thomas Title: Professor of Algebraic Topology College: Robinson College Room: E1.19 Tel: +44 1223 337970 Research Interests: It has long been known that the existence of certain geometric structures on smooth manifolds imposes topological constraints. A deeper question is to ask whether these suffice, and if not, what additional conditions are needed. Examples include Riemannian metrics (with positive scalar, Ricci or sectional curvatures), contact and symplectic forms. In attempting to solve these problems interesting arithmetic questions arise - for example on the role of cubic forms in the construction of symplectic 6-manifolds. Other interests: group cohomology, geometrisation of 3-manifolds, application of topology to number theory. Information provided by webmaster@dpmms.cam.ac.uk

32. Differential Geometry And Physics 2004. differential geometry and Physics. I. Vectors and Curves 1.1 Tangent Vectors 1.2 Curves 1.3 Fundamental Theorem of Curves, II. http://people.uncw.edu/lugo/COURSES/DiffGeom/dg1.htm

Lectures Notes by Gabriel Lugo University of North Carolina at Wilmington Differential Geometry and Physics I. Vectors and Curves 1.1 Tangent Vectors 1.2 Curves 1.3 Fundamental Theorem of Curves II. Differential forms 2.1 1-Forms 2.2 Tensors and Forms of Higher Rank 2.3 Exterior Derivatives 2.4 The Hodge-* Operator III. Connections 3.1 Frames 3.2 Curvilinear Coordinates 3.3 Covariant Derivative 3.4 Cartan Equations IV Surfaces in R 4.1 Manifolds 4.2 First Fundamental form 4.3 Second Fundamental Form 4.4 Curvature Full set (DVI 228K) Full set (PDF 340Kb) Return to Courses home page Gabriel G. Lugo, lugo@uncw.edu Last updated April 10, 2004

33. Differential Geometry And Topology - Wikipedia, The Free Encyclopedia differential geometry and topology. (Redirected from differential geometry). Branches of differential geometry/topology. Contact geometry. http://en.wikipedia.org/wiki/Differential_geometry

Differential geometry and topology From Wikipedia, the free encyclopedia. (Redirected from Differential geometry In mathematics differential topology is the field dealing with differentiable functions on differentiable manifolds . It arises naturally from the study of the theory of differential equations Differential geometry is the study of geometry using calculus . These fields are adjacent, and have many applications in physics , notably in the theory of relativity . Together they make up the geometric theory of differentiable manifolds - which can also be studied directly from the point of view of dynamical systems Table of contents 1 Intrinsic versus extrinsic 2 Technical requirements 3 Branches of differential geometry/topology 3.1 Contact geometry ... edit Intrinsic versus extrinsic Initially and up to the middle of the nineteenth century , differential geometry was studied from the extrinsic point of view: curves surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions). The simplest results are those in the differential geometry of curves . Starting with the work of Riemann , the intrinsic point of view was developed, in which one cannot speak of moving 'outside' the geometric object because it is considered as given in a free-standing way.

34. [math/9201272] Dynamics In One Complex Variable: Introductory Lectures These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself. The reader is assumed to be familiar with the rudiments of complex variable theory and of twodimensional differential geometry. http://arxiv.org/abs/math.DS/9201272

Mathematics, abstract math.DS/9201272 From: John W. Milnor [ view email ] Date: Fri, 20 Apr 1990 (394kb) Dynamics in one complex variable: introductory lectures Authors: John W. Milnor Report-no: Stony Brook IMS 1990/5 Subj-class: Dynamical Systems; Complex Variables These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. They are based on introductory lectures given at Stony Brook during the Fall Term of 1989-90. These lectures are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

35. Differential Geometry And Topology - Wikipedia, The Free Encyclopedia differential geometry and topology. From Wikipedia, the free encyclopedia. Branches of differential geometry/topology. Contact geometry. http://en.wikipedia.org/wiki/Differential_geometry_and_topology

Differential geometry and topology From Wikipedia, the free encyclopedia. In mathematics differential topology is the field dealing with differentiable functions on differentiable manifolds . It arises naturally from the study of the theory of differential equations Differential geometry is the study of geometry using calculus . These fields are adjacent, and have many applications in physics , notably in the theory of relativity . Together they make up the geometric theory of differentiable manifolds - which can also be studied directly from the point of view of dynamical systems Table of contents 1 Intrinsic versus extrinsic 2 Technical requirements 3 Branches of differential geometry/topology 3.1 Contact geometry ... edit Intrinsic versus extrinsic Initially and up to the middle of the nineteenth century , differential geometry was studied from the extrinsic point of view: curves surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions). The simplest results are those in the differential geometry of curves . Starting with the work of Riemann , the intrinsic point of view was developed, in which one cannot speak of moving 'outside' the geometric object because it is considered as given in a free-standing way.

36. Differential Geometry Group differential geometry Group, Staff. Yorkshire differential geometry Days. differential geometry Links. The Geometry Center. The Bibliography of Harmonic Morphisms. http://www.maths.leeds.ac.uk/Pure/geometry/

University of Leeds School of Maths. Pure Maths Differential Geometry Group Staff Dr S. Carter Professor J. Eells, (honorary visiting fellow) Dr K. Houston Dr J. M. Speight Dr A. West (retired) Professor J. C. Wood Research students K. Al-Banawi J.A. McGlade Background Differential geometry is the study of curves and surfaces in space, their generalisations to higher dimensions (manifolds), and their transformations. Further details of individual staff's research interests can be found on their homepages, accessed by clicking the names above. Seminars In April 2000 the group hosted the very successful Workshop on Harmonic Maps and Curvature Properties of Submanifolds, 2. A list of participants, with e-mail addresses, is available here. Yorkshire Differential Geometry Days Differential Geometry Links The Geometry Center The Bibliography of Harmonic Morphisms The Atlas of Harmonic Morphisms Differential Geometry Preprints ... Visual Dictionary of Special Plane Curves Lecture notes in Differential Geometry An introduction to Riemannian Geometry (By S. Gudmundsson).

37. Yorkshire Differential Geometry Day Yorkshire differential geometry Day at Leeds, Yorkshire differential geometry Days are supported by a Scheme 3 grant from the London Mathematical Society. http://www.maths.leeds.ac.uk/pure/geometry/ydgd/dgday.html

Yorkshire Differential Geometry Day at Leeds Wednesday 5 May 2004 10.30 - Coffee outside Mathematics common room, level 9 11.00 - John C. Wood (Leeds) Jacobi fields along harmonic maps 13.15 - Madeeha Khalid (Warwick) K3 correspondences 14.30 - Brendan Guilfoyle (IT Tralee) Geometric optics and the Casimir effect 15.30 - Tea outside Mathematics common room, level 9 16.00 - Christoph Bohle (TU Berlin) Conformal tori in S and integrable systems All interested are welcome to attend. All lectures in Room G23, the Baines Wing. Dinner will be organized at a local restaurant. Please let Martin Speight ( speight@maths.leeds.ac.uk ) know if you intend to arrive by car. For information on the location of the University and a Campus Map, please consult the web page: http://tldynamic.leeds.ac.uk/leisure/alphabet.asp Yorkshire Differential Geometry Days are supported by a Scheme 3 grant from the London Mathematical Society. More information on the series is available at: http://www.amsta.leeds.ac.uk/pure/geometry/ydgd University of Leeds School of Maths. Pure Maths ... Diff. Geom. Group This page is maintained by J.M. Speight

38. Special Structures In Differential Geometry University of Durham; Monday 30th July to Thursday 9th August, 2001. http://www.imada.sdu.dk/~swann/Durham.html

This page has moved to http://www.imada.sdu.dk/~swann/Durham/ If your browser supports it you will automatically be redirected in 10 seconds.

39. Sfb 288 Home Page Translate this page Sonderforschungsbereich 288 differential geometry and Quantum Physics 1992 - 2003. Webmaster wwwop@sfb288.math.tu-berlin.de. Copyright http://www-sfb288.math.tu-berlin.de/

Home About Us Research People ... Impressum Sonderforschungsbereich 288 Differential Geometry and Quantum Physics Webmaster: wwwop@sfb288.math.tu-berlin.de TU-Berlin Mathematik , MA 8-3, Strasse des 17 Juni 136, 10623 Berlin

40. Differential Geometry -- From MathWorld differential geometry. differential geometry is the study of Riemannian manifolds. Differential Handbook of differential geometry, Vol. 1 http://mathworld.wolfram.com/DifferentialGeometry.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Differential Geometry General Differential Geometry ... Budney Differential Geometry Differential geometry is the study of Riemannian manifolds . Differential geometry deals with metrical notions on manifolds , while differential topology deals with those nonmetrical notions of manifolds Differential Topology search Dillen, F. J. E. and Verstraelen, L. C.A. (Eds.). Handbook of Differential Geometry, Vol. 1. Amsterdam, Netherlands: North-Holland, 2000. Eisenhart, L. P. A Treatise on the Differential Geometry of Curves and Surfaces. New York: Dover, 1960. Graustein, W. C. Differential Geometry. New York: Dover, 1966. Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997. Kreyszig, E.

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