An introduction to Riemannian geometry : with applications to mechanics and relativity
著者
書誌事項
An introduction to Riemannian geometry : with applications to mechanics and relativity
（Universitext）
Springer, c2014
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Differentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.
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