An Introduction to Differentiable Manifolds and Riemannian Geometry
Author:
Publisher: Academic Press
Published: 1975-08-22
Total Pages: 441
ISBN-13: 0080873790
DOWNLOAD EBOOKAn Introduction to Differentiable Manifolds and Riemannian Geometry
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An Introduction to Differential Manifolds
Author: Jacques Lafontaine
Publisher: Springer
Published: 2015-07-29
Total Pages: 408
ISBN-13: 3319207350
DOWNLOAD EBOOKThis 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.
Differential and Riemannian Manifolds
Author: Serge Lang
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 376
ISBN-13: 1461241820
DOWNLOAD EBOOKThis 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.).
Introduction to Riemannian Manifolds
Author: John M. Lee
Publisher: Springer
Published: 2019-01-02
Total Pages: 447
ISBN-13: 3319917552
DOWNLOAD EBOOKThis 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.
Riemannian Manifolds
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 232
ISBN-13: 0387227261
DOWNLOAD EBOOKThis 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.
Manifolds and Differential Geometry
Author: Jeffrey Marc Lee
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 690
ISBN-13: 0821848151
DOWNLOAD EBOOKDifferential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
An Introduction to Differentiable Manifolds and Riemannian Geometry
Author:
Publisher: Academic Press
Published: 1986-04-21
Total Pages: 447
ISBN-13: 0080874398
DOWNLOAD EBOOKAn Introduction to Differentiable Manifolds and Riemannian Geometry
An Introduction to Riemannian Geometry
Author: Leonor Godinho
Publisher: Springer
Published: 2014-07-26
Total Pages: 476
ISBN-13: 3319086669
DOWNLOAD EBOOKUnlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
An Introduction to Manifolds
Author: Loring W. Tu
Publisher: Springer Science & Business Media
Published: 2010-10-05
Total Pages: 426
ISBN-13: 1441974008
DOWNLOAD EBOOKManifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Foundations of Differentiable Manifolds and Lie Groups
Author: Frank W. Warner
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 283
ISBN-13: 1475717997
DOWNLOAD EBOOKFoundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.
