Projective Differential Geometry Of A System Of Linear Differential Equations Of The First Order
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Projective Differential Geometry Of A System Of Linear Differential Equations Of The First Order
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Author : Arthur Rudolph Jerbert
language : en
Publisher:
Release Date : 1927
Projective Differential Geometry Of A System Of Linear Differential Equations Of The First Order written by Arthur Rudolph Jerbert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Differential equations categories.
Projective Differential Geometry Of Curves And Ruled Surfaces
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Author : Ernest Julius Wilczynski
language : en
Publisher:
Release Date : 1961
Projective Differential Geometry Of Curves And Ruled Surfaces written by Ernest Julius Wilczynski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Geometry, Differential categories.
Symmetries And Overdetermined Systems Of Partial Differential Equations
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Author : Michael Eastwood
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-23
Symmetries And Overdetermined Systems Of Partial Differential Equations written by Michael Eastwood and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-23 with Mathematics categories.
This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Aspects Of Overdetermined Systems Of Partial Differential Equations In Projective And Conformal Geometry
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Author : Matthew James Randall
language : en
Publisher:
Release Date : 2013
Aspects Of Overdetermined Systems Of Partial Differential Equations In Projective And Conformal Geometry written by Matthew James Randall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Conformal geometry categories.
This thesis discusses aspects of overdetermined systems of partial differential equations (PDEs) in projective and conformal geometry. The first part deals with projective differential geometry. A projective surface is a 2-dimensional smooth manifold equipped with a projective structure i.e. a class of torsion-free affine connections that have the same geodesics as unparameterised curves. Given any projective surface we can ask whether it admits a torsion-free affine connection (in its projective class) that has skew-symmetric Ricci tensor. This is equivalent to solving a particular overdetermined system of semi-linear partial differential equations. It turns out that there are local obstructions to solving the system of PDEs in two dimensions. These obstructions are constructed out of local invariants of the projective structure. We give examples of projective surfaces that admit skew-symmetric Ricci tensor and examples that do not because of nonvanishing obstructions. We relate projective surfaces admitting skew-symmetric Ricci tensor to 3-webs in 2 dimensions. We also give examples of projective structures in higher dimensions that admit skew-symmetric Ricci tensor. The second part of the thesis deals with conformal differential geometry. On Mobius surfaces introduced in [5], we can define an analogous overdetermined system of semi-linear PDEs as in the projective case. This is called the scalar-flat Mobius Einstein-Weyl equation and is conformally invariant. We derive local algebraic constraints for Mobius surfaces to admit a solution to this equation and give local obstructions. These obstructions are similarly constructed out of local conformal invariants of the Mobius structure. Again we provide examples of Mobius surfaces that admit a solution and examples that do not because of non-vanishing obstructions. Finally, we also investigate the conformally Einstein equation on Mobius surfaces and derive obstructions. In contrast to the previous two equations, the conformally Einstein equation is linear.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Cartan For Beginners
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Author : Thomas Andrew Ivey
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Cartan For Beginners written by Thomas Andrew Ivey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.
Nonlinear Partial Differential Equations In Differential Geometry
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Author : Robert Hardt
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Nonlinear Partial Differential Equations In Differential Geometry written by Robert Hardt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics
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Author : Xerox University Microfilms
language : en
Publisher:
Release Date : 1973
Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics written by Xerox University Microfilms and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Dissertations, Academic categories.
Differential Geometry Partial Differential Equations On Manifolds
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Differential Geometry Partial Differential Equations On Manifolds written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem
Partial Differential Equations
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Author : Shiing-shen Chern
language : en
Publisher: Springer
Release Date : 2006-11-14
Partial Differential Equations written by Shiing-shen Chern and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.