An Introduction to Riemannian Geometry

With Applications to Mechanics and Relativity

Nonfiction, Science & Nature, Mathematics, Geometry, Science, Physics, Mathematical Physics
Cover of the book An Introduction to Riemannian Geometry by Leonor Godinho, José Natário, Springer International Publishing
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Author: Leonor Godinho, José Natário ISBN: 9783319086668
Publisher: Springer International Publishing Publication: July 26, 2014
Imprint: Springer Language: English
Author: Leonor Godinho, José Natário
ISBN: 9783319086668
Publisher: Springer International Publishing
Publication: July 26, 2014
Imprint: Springer
Language: English

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.

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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.

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