Tensors and Riemannian Geometry: With Applications to Differential Equations (De Gruyter Textbook)

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. Content: Table of ContentsPart I Tensors and Riemannian Spaces 1 Preliminaries 2 Conservation laws 3 Introduction of tensors and Riemannian spaces4 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 BibliographyIndex This Graduate Textbook Begins By Introducing Tensors And Riemannian Spaces, And Then Elaborates Their Application In Solving Second-order Differential Equations, And Ends With Introducing Theory Of Relativity And De Sitter Space. Based On 40 Years Of Teaching Experience, The Author Compiles A Well-developed Collection Of Examples And Exercises To Facilitate The Reader S Learning.