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An Introduction to Riemannian Geometry With Applications to Mechanics and Relativity / by Leonor Godinho, Jose Natario.

By: Godinho, Leonor [author.].
Contributor(s): Natario, Jose [author.].
Material type: TextTextSeries: Universitext: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: x, 467 pages; E 59.99 ill.; 23 cms.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319086651 (pbk).Subject(s): Mathematics | Global differential geometry | Mechanics | Mathematics | Differential Geometry | Mathematical Physics | Mechanics | Classical and Quantum Gravitation, Relativity TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 516.36
Contents:
Differentiable Manifolds -- Differential Forms -- Riemannian Manifolds -- Curvature -- Geometric Mechanics -- Relativity.
Summary: 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.
List(s) this item appears in: 2016-10-31

Includes index.

Differentiable Manifolds -- Differential Forms -- Riemannian Manifolds -- Curvature -- Geometric Mechanics -- Relativity.

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.