Semi-Riemannian Geometry With Applications to Relativity

Nonfiction, Science & Nature, Mathematics, Geometry, Science
Cover of the book Semi-Riemannian Geometry With Applications to Relativity by Barrett O'Neill, Elsevier Science
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Author: Barrett O'Neill ISBN: 9780080570570
Publisher: Elsevier Science Publication: July 29, 1983
Imprint: Academic Press Language: English
Author: Barrett O'Neill
ISBN: 9780080570570
Publisher: Elsevier Science
Publication: July 29, 1983
Imprint: Academic Press
Language: English

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.

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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.

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