Symmetries of spacetimes and Riemannian manifolds

Authors:Krishan L. Duggal, Ramesh Chandra Sharma

Summary:"This book provides up-to-date information on metric (i.e. Killing, homothetic and conformal), connection (i.e. affine, conformal and projective), curvature collineations and curvature inheritance symmetries. It is the first-ever attempt to present a comprehensive account of a very large number of papers on symmetries of spacetimes and Riemannian manifolds. An attempt has been made to present the Lie group/algebra structures of symmetry vectors, their kinematics/dynamics, compact hypersurfaces (dealing with the initial value problem in general relativity) and lightlike hypersurfaces. This book also contains the latest information on symmetries of Kaehler, contact and globally framed manifolds."--Jacket

Edition:View all formats and editions

Series:

Mathematics and its applications (Kluwer Academic Publishers), v. 487

Physical Description:x, 214 pages : illustrations ; 25 cm.

ISBN:

9780792357933, 9780000792358, 0792357930, 0000792357

OCLC Number / Unique Identifier:41285073

Subjects:

Espai i temps

Riemann, Varietats de

Variétés de Riemann

Additional Physical Form Entry:

Online version:

Symmetries of spacetimes and Riemannian manifolds.

Duggal, Krishan L., 1929-

654755575

Contents:

Dedication

(4)

Preface

1 Preliminaries

(9)

1.1 Semi-Euclidean Vector Spaces

(3)

1.2 Subspaces of Minkowski Spaces

(2)

1.3 Electromagnetism in R^(4)(1)

(3)

1.4 Algebraic Structures

(1)

2 Semi-Riemannian Manifolds and Hypersurfaces

(26)

2.1 Differentiable Manifolds

(1)

2.2 Tensor Fields

(4)

2.3 Covariant and Exterior Derivatives

(3)

2.4 Semi-Riemannian Geometry

(4)

2.5 Semi-Riemannian Hypersurfaces

(2)

2.6 Null Curves of Lorentz Manifolds

(5)

2.7 Lightlike Hypersurfaces of Lorentz Manifolds

(7)

3 Lie Derivatives and Symmetry Groups

(20)

3.1 Integral Curves and Lie Derivatives

(4)

3.2 Lie Groups and Lie Algebras

(3)

3.3 Transformation Groups

(2)

3.4 Isometric and Conformal Symmetries

(6)

3.5 Affine, Projective and Curvature Collineations

(5)

4 Spacetimes of General Relativity

(23)

4.1 Spacetimes and Kinematic Quantities

(5)

4.2 Matter Tensor and Einstein's Field Equations

(4)

4.3 Spacetimes of Constant Curvature

(5)

4.4 Spacially Homogeneous Cosmological Models

(2)

4.5 Asymptotically Flat Spacetimes

(5)

4.6 Plane Wave Solutions

(2)

5 Killing and Affine Killing Vector Fields

(24)

5.1 Divergence Theorems

(2)

5.2 Killing Vector Fields on Riemannian Manifolds

(5)

5.3 Killing and Affine Symmetries on Semi-Riemannian Manifolds

(1)

5.4 Killing Symmetries in General relativity

(9)

5.5 Affine Collineations in General Relativity

(7)

6 Homothetic and Conformal Symmetries

103

(31)

6.1 Homothetic Symmetry in General Relativity

103

(6)

6.2 Homothetic Symmetry and Cauchy Surfaces

109

(6)

6.3 Homothetic Symmetry and Compact Hypersurfaces

115

(2)

6.4 Homothetic Symmetry and Lightlike Hypersurfaces

117

(2)

6.5 Conformal Motions in General Relativity

119

(5)

6.6 Relativistic Fluids and Conformal Symmetry

124

(7)

6.7 Conformal Motions in Riemannian Manifolds

131

(3)

7 Connection and Curvature Symmetries

134

(22)

7.1 Conformal Collineations

134

(6)

7.2 Conformal collineations in Relativity

140

(2)

7.3 Projective Collineations

142

(3)

7.4 Projective collineations in Relativity

145

(2)

7.5 Curvature Collineations

147

(5)

7.6 Ricci Collineations in Relativity

152

(4)

8 Symmetry Inheritance

156

(17)

8.1 Inheriting CKV Fields

156

(5)

8.2 Curvature Inheritance

161

(6)

8.3 Ricci Inheritance in Relativity

167

(6)

9 Symmetries of Some Geometric Structures

173

(20)

9.1 Kaehler Manifolds

173

(3)

9.2 Symmetries of Kaehler Manifolds

176

(2)

9.3 Contact Manifolds

178

(4)

9.4 Symmetries of Contact Manifolds

182

(4)

9.5 Globally Framed Manifolds

186

(3)

9.6 Symmetries of Framed Manifolds

189

(2)

9.7 Killing Horizon

191

(2)

A The Petrov Classification

193

(2)

Bibliography

195

(13)

Index

208

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