Differential And Riemannian Manifolds

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241829

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Differential and Riemannian Manifolds by Serge Lang Pdf

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

Author : Jacques Lafontaine
Publisher : Springer
Page : 395 pages
File Size : 45,7 Mb
Release : 2015-07-29
Category : Mathematics
ISBN : 9783319207353

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An Introduction to Differential Manifolds by Jacques Lafontaine Pdf

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Author : Jeffrey M. Lee
Publisher : American Mathematical Society
Page : 671 pages
File Size : 51,9 Mb
Release : 2022-03-08
Category : Mathematics
ISBN : 9781470469825

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Manifolds and Differential Geometry by Jeffrey M. Lee Pdf

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.

Author : Ovidiu Calin,Der-Chen Chang
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 43,9 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780817644215

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Geometric Mechanics on Riemannian Manifolds by Ovidiu Calin,Der-Chen Chang Pdf

* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402650

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Differential Manifolds by Serge Lang Pdf

The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26]).

Author : William Munger Boothby
Publisher : Gulf Professional Publishing
Page : 444 pages
File Size : 41,6 Mb
Release : 2003
Category : Mathematics
ISBN : 0121160513

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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised by William Munger Boothby Pdf

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

Author : QUDDUS KHAN
Publisher : PHI Learning Pvt. Ltd.
Page : 325 pages
File Size : 46,7 Mb
Release : 2012-09-03
Category : Mathematics
ISBN : 9788120346505

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DIFFERENTIAL GEOMETRY OF MANIFOLDS by QUDDUS KHAN Pdf

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, while trying to answer them using calculus techniques. The geometry of differentiable manifolds with structures is one of the most important branches of modern differential geometry. This well-written book discusses the theory of differential and Riemannian manifolds to help students understand the basic structures and consequent developments. While introducing concepts such as bundles, exterior algebra and calculus, Lie group and its algebra and calculus, Riemannian geometry, submanifolds and hypersurfaces, almost complex manifolds, etc., enough care has been taken to provide necessary details which enable the reader to grasp them easily. The material of this book has been successfully tried in classroom teaching. The book is designed for the postgraduate students of Mathematics. It will also be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and cosmology, and other applied areas. KEY FEATURES  Provides basic concepts in an easy-to-understand style.  Presents the subject in a natural way.  Follows a coordinate-free approach.  Includes a large number of solved examples and illuminating illustrations.  Gives notes and remarks at appropriate places.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418

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Fundamentals of Differential Geometry by Serge Lang Pdf

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

Author : John M. Lee
Publisher : Springer
Page : 437 pages
File Size : 49,9 Mb
Release : 2019-01-02
Category : Mathematics
ISBN : 9783319917559

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Introduction to Riemannian Manifolds by John M. Lee Pdf

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 52,7 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227269

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Riemannian Manifolds by John M. Lee Pdf

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author : Uday Chand De,Absos Ali Shaikh
Publisher : Alpha Science International, Limited
Page : 320 pages
File Size : 45,9 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015070764629

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Differential Geometry of Manifolds by Uday Chand De,Absos Ali Shaikh Pdf

Differential Geometry of Manifolds discusses the theory of differentiable and Riemannian manifolds to help students understand the basic structures and consequent developments. Since the tangent vector plays a crucial role in the study of differentiable manifolds, this idea has been thoroughly discussed. In the theory of Riemannian geometry some new proofs have been included to enable the reader understand the subject in a comprehensive and systematic manner. This book will also benefit the postgraduate students as well as researchers working in the field of differential geometry and its applications to general relativity and cosmology.

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 53,5 Mb
Release : 2000
Category : Brownian motion processes
ISBN : 9780821838396

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An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 560 pages
File Size : 41,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821814949

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Differential Geometry: Partial Differential Equations on Manifolds by Robert Everist Greene,Shing-Tung Yau Pdf

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

Author : Pierre E. Conner
Publisher : American Mathematical Soc.
Page : 64 pages
File Size : 43,9 Mb
Release : 1956
Category : Differential forms
ISBN : 9780821812204

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The Neumann's Problem for Differential Forms on Riemannian Manifolds by Pierre E. Conner Pdf

Author : Stephen Lovett
Publisher : CRC Press
Page : 367 pages
File Size : 42,8 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9780429607820

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Differential Geometry of Manifolds by Stephen Lovett Pdf

Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a both streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics. The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, string theory. The Second Edition of this successful textbook offers several notable points of revision. New to the Second Edition: New problems have been added and the level of challenge has been changed to the exercises Each section corresponds to a 60-minute lecture period, making it more user-friendly for lecturers Includes new sections which provide more comprehensive coverage of topics Features a new chapter on Multilinear Algebra