Basic Elements of Differential Geometry and Topology

Inhaltsverzeichnis

• I. Basic Concepts of Differential Geometry.
• II. Tensors. Riemannian Geometry.
• III. Basic Elements of Topology.
• Appendices.
• Appendix 1 The Simplest Groups of Transformations of Euclidean and Non-Euclidean Spaces.
• Appendix 2 Some Elements of Modern Concepts of the Geometry of the Real World.
• Appendix 3 Crystallographic Croups.
• Appendix 4 Homology Groups and Methods of their Calculation.
• Appendix 5 The Theory of Geodesics, Second Variation and Variational Calculus.
• Appendix 6 Basic Geometric Properties of the Lobachevskian Plane.
• Appendix 7 Selected Exerices on the Material of the Course.
• Additional Material.
• References.