TY  - BOOK
AU  - Godinho,Leonor
AU  - Natario,Jose
TI  - Introduction to Riemannian geometry : : with applications to mechanics and relativity 
T2  - Universitext 
SN  - 9783319086651
U1  - 516.373 23
PY  - 2014///
CY  - Switzerland
PB  - Springer
KW  - Riemannian Geometry.
KW  - Differential Geometry.
KW  - Mathematical Physics
N1  - Includes bibliographical references and index; 1. Differentiable Manifolds --
2. Differential Forms --
3. Riemannian Manifolds --
4. Curvature --
5. Geometric Mechanics --
6. Relativity--
7. Solutions to selected exercises--
References--
Index
N2  - 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.
ER  -