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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 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.

Riemannian Geometry

2006-04-10 Mathematics
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Release : 2006-04-10
Genre : Mathematics
Kind : eBook
Book Rating : 576/5 ( reviews)

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Book Synopsis Riemannian Geometry by : Isaac Chavel

Download or read book Riemannian Geometry written by Isaac Chavel. This book was released on 2006-04-10. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

An Introduction to Riemannian Geometry and the Tensor Calculus

1938 Calculus of tensors
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Release : 1938
Genre : Calculus of tensors
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis An Introduction to Riemannian Geometry and the Tensor Calculus by : Charles Ernest Weatherburn

Download or read book An Introduction to Riemannian Geometry and the Tensor Calculus written by Charles Ernest Weatherburn. This book was released on 1938. Available in PDF, EPUB and Kindle. Book excerpt:

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