Universitext

An Introduction to Riemannian Geometry

With Applications to Mechanics and Relativity

Authors: Godinho, Leonor, Natário, José

  • 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
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eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-08666-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-08665-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

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).

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)


Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-08666-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-08665-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Riemannian Geometry
Book Subtitle
With Applications to Mechanics and Relativity
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-08666-8
DOI
10.1007/978-3-319-08666-8
Softcover ISBN
978-3-319-08665-1
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 467
Number of Illustrations and Tables
60 b/w illustrations
Topics