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Semi-Riemannian Geometry : With Applications to Relativity

Semi-Riemannian Geometry : With Applications to Relativity - 83 edition

ISBN13: 978-0125267403

Cover of Semi-Riemannian Geometry : With Applications to Relativity 83 (ISBN 978-0125267403)
ISBN13: 978-0125267403
ISBN10: 0125267401
Cover type: Print On Demand
Edition/Copyright: 83
Publisher: Academic Press, Inc.
Published: 1983
International: No

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Semi-Riemannian Geometry : With Applications to Relativity - 83 edition

ISBN13: 978-0125267403

Barrett O'Neill

ISBN13: 978-0125267403
ISBN10: 0125267401
Cover type: Print On Demand
Edition/Copyright: 83
Publisher: Academic Press, Inc.

Published: 1983
International: No
Summary

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.

Author Bio

O'Niell, Barrett : University of California-Los Angeles

Table of Contents

Manifold Theory.
Tensors.
Semi-Riemannian Manifolds.
Semi-Riemannian Submanifolds.
Riemannian and Lorentz Geometry.
Special Relativity.
Constructions.
Symmetry and Constant Curvature.
Isometries.
Calculus of Variations.
Homogeneous and Symmetric Spaces.
General Relativity; Cosmology.
Schwarzschild Geometry.
Causality in Lorentz Manifolds.


Appendixes.
Index.

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