Authors:
- Presents a self-contained treatment of Riemannian geometry and applications to mechanics and relativity in one book
- Conveys nontrivial results in general relativity (such as the Hawking and Penrose singularity theorems) which are not usually treated in introductory texts
- Contains detailed solutions to many of the 300 exercises to help students test and consolidate their understanding
- Includes a summary of all the main definitions and results from the necessary background material in differential calculus, algebra and topology
- Includes supplementary material: sn.pub/extras
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Universitext (UTX)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
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)
Authors and Affiliations
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Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
Leonor Godinho, José Natário
About the authors
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 mathematics at Instituto Superior Técnico (Universidade de Lisboa). He regularly lectures on differential and Riemannian geometry, geometric mechanics and mathematical relativity. His research focuses on general relativity, a subject on which he has published many research papers and a book, “General Relativity Without Calculus” (Springer, 2011).
Bibliographic Information
Book Title: An Introduction to Riemannian Geometry
Book Subtitle: With Applications to Mechanics and Relativity
Authors: Leonor Godinho, José Natário
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-08666-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-08665-1Published: 07 August 2014
eBook ISBN: 978-3-319-08666-8Published: 26 July 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: X, 467
Number of Illustrations: 60 b/w illustrations
Topics: Differential Geometry, Mathematical Physics, Classical Mechanics, Classical and Quantum Gravitation, Relativity Theory