An Introduction to Riemannian Geometry
With Applications to Mechanics and Relativity
Authors: Godinho, Leonor, Natário, José
Free Preview- 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
Buy this book
- 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)
-
-
Differentiable Manifolds
Pages 1-59
-
Differential Forms
Pages 61-94
-
Riemannian Manifolds
Pages 95-122
-
Curvature
Pages 123-164
-
Geometric Mechanics
Pages 165-250
-
Table of contents (7 chapters)
- Download Preface 1 PDF (52.4 KB)
- Download Sample pages 2 PDF (358.8 KB)
- Download Table of contents PDF (144.7 KB)
- geometria_solutions
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
- 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
- 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
- 60 b/w illustrations
- Topics
