Projectively flat Finsler spaces with \((\alpha{},\beta{})\)-metric
type: Item
instance of: scholarly article
title: Projectively flat Finsler spaces with \((\alpha{},\beta{})\)-metric
zbMATH Open document ID: 0764.53015
DOI: 10.1016/0034-4877(91)90035-L
published in: Reports on Mathematical Physics
publication date: 1993-01-16T00:00:00Z
review text: The \((\alpha,\beta)\)-metric is a Finsler metric which is constructed from a Riemannian metric \(\alpha\) and a differential 1-form \(\beta\). A Finsler space is called projectively flat, or with rectilinear geodesic, if the space is covered by coordinate neighbourhoods in which the geodesics can be represented by \(n-1\) linear equations of the coordinates. Such a coordinate system is called rectilinear. In the present paper the author considers the projective flatness of Finsler spaces with \((\alpha,\beta)\)-metric. Projective flatness of the Kropina space and a special generalized Kropina space are also studied.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 89979
zbMATH Keywords: \((\alpha,\beta)\)-metric
zbMATH Keywords: rectilinear geodesic
zbMATH Keywords: Kropina space
author: Makoto Matsumoto
MaRDI profile type: Publication
cites work: Über Finslersche und Cartansche Geometrie. IV. Projektivkrümmung allgemeiner affiner Räume und Finslerscher Räume skalarer Krümmung
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cites work: On Finsler spaces with Kropina metric
full work available at URL: 0034-4877(91)90035-l
OpenAlex ID: W2025263645
description: scientific article; zbMATH DE number 89979