Semi-Riemannian Geometry With Applications to Relativity

✍ Scribed by Barrett O'Neill

Publisher: Academic Press
Year: 1983
Tongue: English
Leaves: 471
Series: Pure and Applied Mathematics, Volume 103
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

✦ Table of Contents

Content:
Editorial Page
Page iii

Copyright Page
Page iv

Preface
Pages xi-xii

Notation and Terminology
Page xiii

1. Manifold Theory
Pages 1-33

2. Tensors
Pages 34-53

3. Semi-Riemannian Manifolds
Pages 54-96

4. Semi-Riemannian Submanifolds
Pages 97-125

5. Riemannian and Lorentz Geometry
Pages 126-157

6. Special Relativity
Pages 158-184

7. Constructions
Pages 185-214

8. Symmetry and Constant Curvature
Pages 215-232

9. Isometries
Pages 233-262

10. Calculus of Variations
Pages 263-299

11. Homogeneous and Symmetric Spaces
Pages 300-331

12. General Relativity; Cosmology
Pages 332-363

13. Schwarzschild Geometry
Pages 364-400

14. Causality in Lorentz Manifolds
Pages 401-439

Appendix A Fundamental Groups and Covering Manifolds
Pages 441-445

B Lie Groups
Pages 446-452

C Newtonian Gravitation
Pages 453-455

References
Pages 456-457

Index
Pages 459-468

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