Semi-Riemannian geometry : with applications to relativity /
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...
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Main Authors: | |
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Corporate Authors: | |
Published: |
Academic Press,
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Publisher Address: | New York : |
Publication Dates: | 1983. |
Literature type: | eBook |
Language: | English |
Series: |
Pure and applied mathematics ;
103 |
Subjects: | |
Online Access: |
http://www.sciencedirect.com/science/bookseries/00798169/103 |
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. |
Carrier Form: | 1 online resource (xiii, 468 pages). |
Bibliography: | Includes bibliographical references (pages 456-457) and index. |
ISBN: |
9780080570570 0080570577 |
Index Number: | QA3 |
CLC: | O186.12 |
Contents: | Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorenz 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. Fundamental Groups and Covering Manifolds. Lie Groups. Newtonian Gravitation. |