Semi-Riemannian Geometry With Applications to Relativity

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Academic Press, Jul 29, 1983 - Mathematics - 468 pages
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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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Contents

CHAPTER 1 MANIFOLD THEORY
1
CHAPTER 2 TENSORS
34
CHAPTER 3 SEMIRIEMANNIAN MANIFOLDS
54
CHAPTER 4 SEMIRIEMANNIAN SUBMANIFOLDS
97
CHAPTER 5 RIEMANNIAN AND LORENTZ GEOMETRY
126
CHAPTER 6 SPECIAL RELATIVITY
158
CHAPTER 7 CONSTRUCTIONS
185
CHAPTER 8 SYMMETRY AND CONSTANT CURVATURE
215
CHAPTER 11 HOMOGENEOUS AND SYMMETRIC SPACES
300
CHAPTER 12 GENERAL RELATIVITY COSMOLOGY
332
CHAPTER 13 SCHWARZSCHILD GEOMETRY
364
CHAPTER 14 CAUSALITY IN LORENTZ MANIFOLDS
401
FUNDAMENTAL GROUPS AND COVERING MANIFOLDS
441
LIE GROUPS
446
NEWTONIAN GRAVITATION
453
References
456

CHAPTER 9 ISOMETRIES
233
CHAPTER 10 CALCULUS OF VARIATIONS
263

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About the author (1983)

Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles. He has written two other books in advanced mathematics.

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