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.
- DOI https://doi.org/10.1007/978-3-319-08666-8
- Copyright Information Springer International Publishing Switzerland 2014
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-08665-1
- Online ISBN 978-3-319-08666-8
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
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