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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 517/5 ( reviews)

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Book Synopsis An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised by : William Munger Boothby

Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised written by William Munger Boothby. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: 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

An Introduction to Differentiable Manifolds and Riemannian Geometry

1986-04-21 Mathematics
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Release : 1986-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 398/5 ( reviews)

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Book Synopsis An Introduction to Differentiable Manifolds and Riemannian Geometry by :

Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry written by . This book was released on 1986-04-21. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Differentiable Manifolds and Riemannian Geometry

An Introduction to Differential Manifolds

2015-07-29 Mathematics
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Release : 2015-07-29
Genre : Mathematics
Kind : eBook
Book Rating : 350/5 ( reviews)

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Book Synopsis An Introduction to Differential Manifolds by : Jacques Lafontaine

Download or read book An Introduction to Differential Manifolds written by Jacques Lafontaine. This book was released on 2015-07-29. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Differential and Riemannian Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 820/5 ( reviews)

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Book Synopsis Differential and Riemannian Manifolds by : Serge Lang

Download or read book Differential and Riemannian Manifolds written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.).

Introduction to Riemannian Manifolds

2019-01-02 Mathematics
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Release : 2019-01-02
Genre : Mathematics
Kind : eBook
Book Rating : 552/5 ( reviews)

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Book Synopsis Introduction to Riemannian Manifolds by : John M. Lee

Download or read book Introduction to Riemannian Manifolds written by John M. Lee. This book was released on 2019-01-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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