This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.

Autorentext

Nail H. Ibragimov, Ufa State Aviation Technical University, Russia, Blekinge Institute of Technology, Sweden

Zusammenfassung

"One characteristic of this book is its hands-on approach which favours explicit coordinate calculations over abstract concepts, which reflects the development of the field. The latter is also nicely illustrated by the many illuminating historical and philosophical citations."
R. Steinbauer in: Monatshefte für Mathematik 139 (2019), 383-384

Inhalt

Table of Contents Part I Tensors and Riemannian Spaces 1 Preliminaries 2 Conservation laws 3 Introduction of tensors and Riemannian spaces 4 Motions in Riemannian spaces Part II Riemannian Spaces of Second-Order Equations 5 Riemannian spaces associated with linear PDEs 6 Geometry of linear hyperbolic equations 7 Solution of the initial value problem Part III Theory of Relativity 8 Brief introduction to Relativity 9 Relativity in de Sitter space Bibliography Index