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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.

Riemannian Manifolds

2006-04-06 Mathematics
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Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : 261/5 ( reviews)

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Book Synopsis Riemannian Manifolds by : John M. Lee

Download or read book Riemannian Manifolds written by John M. Lee. This book was released on 2006-04-06. 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.

An Introduction to Riemannian Geometry

2014-07-26 Mathematics
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Release : 2014-07-26
Genre : Mathematics
Kind : eBook
Book Rating : 669/5 ( reviews)

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Book Synopsis An Introduction to Riemannian Geometry by : Leonor Godinho

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho. This book was released on 2014-07-26. Available in PDF, EPUB and Kindle. Book excerpt: Unlike 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.

Introduction to Topological Manifolds

2006-04-06 Mathematics
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Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)

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

Download or read book Introduction to Topological Manifolds written by John M. Lee. This book was released on 2006-04-06. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

An Introduction to the Analysis of Paths on a Riemannian Manifold

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 393/5 ( reviews)

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

Download or read book An Introduction to the Analysis of Paths on a Riemannian Manifold written by Daniel W. Stroock. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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