Finsler geometry, relativity and gauge theories
type: Item
instance of: scholarly article
title: Finsler geometry, relativity and gauge theories
zbMATH Open document ID: 0576.53001
published in: Fundamental Theories of Physics
publication date: 1985-01-01T00:00:00Z
review text: The purpose of the book is to elaborate a systematic study of the main techniques for extending general relativity based on the geometry of Finsler spaces. The first two chapters stand for a rapid introduction to Finsler geometry. Chapter 3 is concerned with the general theory of invariance identities and its applications to constructions of connection coefficients and fundamental tensor densities. In chapters 4 and 5 two Finslerian approaches are formulated to obtain generalizations of the physical field equations. The first approach is based on the concept of osculation, according to which a vector field \(y^ i(x)\) is going to be substituted for the directional variable \(y^ i\) any time when a Lagrangian density is constructed. The second approach is based on the notion of indicatrix in a Finsler space, which is in fact a hypersurface in the tangent space to a Finsler space, defined by the equation \(F(x,y)=1\), where F is the Finslerian metric function. Some problems of classical mechanics are studied in chapter 6 from the Finslerian viewpoint. Chapter 7 is dealing with Finslerian extension of the special principle of relativity and Finslerian kinematics. There are added two appendices. In the first one the author describes the Rund theory with respect to the concept of direction-dependent connection. The second one is concerned with a generalization of both, the Finslerian gauge ideas from chapter 5 and from the first appendix. Each chapter ends with some notes and problems. Finally, the author provides to the reader an up to day list of publications on Finsler geometry. We conclude by saying that Asanov's book is an important contribution to literature and should benefit both experts and novices in applications of Finsler geometry.
Mathematics Subject Classification ID: 53-02
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83D05
zbMATH DE Number: 3921387
zbMATH Keywords: osculation concept
zbMATH Keywords: indicatrix
zbMATH Keywords: general relativity
zbMATH Keywords: Finsler spaces
zbMATH Keywords: direction-dependent connection
zbMATH Keywords: Finsler geometry
author: Gennadii S. Asanov
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3921387