Das Tensors

The Mathematics of Relativity Theory and Continuum Mechanics
1. Auflage 2007
ISBN: 978-0-387-69469-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 290 Seiten

Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.

Anadi Das is a Professor Emeritus at Simon Fraser University, British Columbia, Canada.  He earned his Ph.D. in Mathematics and Physics from the National University of Ireland and his D.Sc. from Calcutta University.  He has published numerous papers in publications such as the Journal of Mathematical Physics and Foundation of Physics.  His book entitled The Special Theory of Relativity: A Mathematical Exposition was published by Springer in 1993.

Autoren/Hrsg.

Das, Anadi Jiban

Inhaltsverzeichnis

1;Preface;6
2;Finite-Dimensional Vector Spaces and Linear Mappings;12
2.1;Fields;12
2.2;Finite-Dimensional Vector Spaces;14
2.3;Linear Mappings of a Vector Space;20
2.4;Dual or Covariant Vector Spaces;22
3;Tensor Algebra;27
3.1;Second-Order Tensors;27
3.2;Higher-Order Tensors;35
3.3;Exterior or Grassmann Algebra;42
3.4;Inner Product Vector Spacesand the Metric Tensor;53
4;Tensor Analysis on a Differentiable Manifold;63
4.1;Differentiable Manifolds;63
4.2;Tangent Vectors, Cotangent Vectors, and Parametrized Curves;71
4.3;Tensor Fields over Differentiable Manifolds;80
4.4;Differential Forms and Exterior Derivatives;91
5;Differentiable Manifolds with Connections;103
5.1;The Affine Connection and Covariant Derivative;103
5.2;Covariant Derivatives of Tensors along a Curve;112
5.3;Lie Bracket, Torsion, and Curvature Tensor;118
6;Riemannian and Pseudo-Riemannian Manifolds;132
6.1;Metric Tensor, Christoffel Symbols, and Ricci Rotation Coefficients;132
6.2;Covariant Derivatives and the Curvature Tensor;146
6.3;Curves, Frenet-Serret Formulas,and Geodesics;168
6.4;Special Coordinate Charts;192
7;Special Riemannian and Pseudo-Riemannian Manifolds;211
7.1;Flat Manifolds;211
7.2;The Space of Constant Curvature;216
7.3;Einstein Spaces;225
7.4;Conformally Flat Spaces;227
8;Hypersurfaces, Submanifolds, and Extrinsic Curvature;236
8.1;Two-Dimensional Surfaces Embedded in a Three-Dimensional Space;236
8.2;(N-1)-Dimensional Hypersurfaces;244
8.3;D-Dimensional Submanifolds;256
9;Appendix I Fibre Bundles;267
10;Appendix II Lie Derivatives;268
11;Answers and Hints to Selected Exercises;281
12;References;285
13;List of Symbols;288
14;Index;291