Tensors and Riemannian Geometry: With Applications to Differential Equations

ISBN-13: 9783110379495 / Angielski / Miękka / 2015 / 197 str.

Nail H. Ibragimov;Higher Education Press

Opis

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. "

Recenzje

"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

Spis treści

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

O autorze

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