Table of Contents

Part I Tensors and Riemannian spaces
  1 Preliminaries
   1.1 Vectors in linear spaces
   1.2 Index notationSummation convention
   Exercises
  2 Conservation laws
   2.1 Conservation laws in classical mechanics
   2.2 General discussion of conservation laws
   2.3 Conserved vectors defined by symmetries
   Exercises
  3 Introduction of tensors and Riemannian spaces
   3.1 Tensors
   3.2 Riemannian spaces
   3.3 Application to ODEs
   Exercises
  4 Motions in Riemannian spaces
   4.1 Introduction
   4.2 Isometric motions
   4.3 Conformal motions
   4.4 Generalized motions
   Exercises
Part II Riemannian spaces of second-order equations
  5 Riemannian spaces associated with linear PDEs
   5.1 Covariant form of second-order equations
   5.2 Conformally invariant equations
   Exercises
  6 Geometry of linear hyperbolic equations
   6.1 Generalities
   6.2 Spaces with nontrivial conformal group
   6.3 Standard form of second-order equations
   Exercises
  7 Solution of the initial value problem
   7.1 The Cauchy problem
   7.2 Geodesics in spaces with nontrivial conformal group
   7.3 The Huygens principle
   Exercises
Part III Theory of relativity
  8 Brief introduction to relativity
   8.1 Special relativity
   8.2 The Maxwell equations
   8.3 The Dirac equation
   8.4 General relativity
   Exercises
  9 Relativity in de Sitter space
   9.1 The de Sitter space
   9.2 The de Sitter group
   9.3 Approximate de Sitter group.
   9.4 Motion of a particle in de Sitter space
   9.5 Curved wave operator.
   9.6 Neutrinos in de Sitter space
   Exercises
Bibliography
Index

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