An Introduction to Riemannian Geometry
With Applications to Mechanics and Relativity
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Beschreibung
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.
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.
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 Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material
Autor*in
Leonor Godinho
Themen in »An Introduction to Riemannian Geometry«
General Relativity Geometric Mechanics Riemannian Geometry Singularity Theorems
Stimmen zu »An Introduction to Riemannian Geometry«
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)
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