An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity by Leonor GodinhoAn Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity by Leonor Godinho

An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity

byLeonor Godinho, Jos Natário

Paperback | August 7, 2014

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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.

Leonor Godinho is professor at Instituto Superior Técnico (Universidade de Lisboa). She regularly teaches Riemannian geometry, symplectic geometry and introductory geometry courses. Her research activity is focused on symplectic geometry and its connections to algebraic geometry and combinatorics.José Natário is professor of mathematic...
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Title:An Introduction to Riemannian Geometry: With Applications to Mechanics and RelativityFormat:PaperbackDimensions:467 pagesPublished:August 7, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319086650

ISBN - 13:9783319086651

Reviews

Table of Contents

Differentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.

Editorial Reviews

From the book reviews:"The aim of the textbook is twofold. First, it is a concise and self-contained quick introduction to the basics of differential geometry, including differential forms, followed by the main ideas of Riemannian geometry. Second, the last two chapters are devoted to some interesting applications to geometric mechanics and relativity. . the book is well written and also very readable. I warmly recommend it to specialists in mathematics, physics and engineering, especially to Ph.D. students." (Miroslaw Doupovec, zbMATH 1306.53001, 2015)