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Introduction to Riemannian geometry : with applications to mechanics and relativity / Leonor Godinho and Jose Natario.

By: Contributor(s): Material type: TextTextSeries: UniversitextPublication details: Switzerland : Springer, 2014.Description: x, 467 p. ; illustrationsISBN:
  • 9783319086651
Subject(s): DDC classification:
  • 516.373 23 G585
Contents:
1. Differentiable Manifolds -- 2. Differential Forms -- 3. Riemannian Manifolds -- 4. Curvature -- 5. Geometric Mechanics -- 6. Relativity-- 7. Solutions to selected exercises-- References-- Index.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 516.373 G585 (Browse shelf(Opens below)) Available 135803
Total holds: 0

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.

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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