Some constructions of projectively flat Finsler metrics
type: Item
instance of: scholarly article
title: Some constructions of projectively flat Finsler metrics
zbMATH Open document ID: 1115.53048
author: Xiaohuan Mo
author: Chunhong Yang
author: Zhongmin Shen
published in: Science in China. Series A
publication date: 2007-01-24T00:00:00Z
review text: The authors study a projectively flat Finsler metric the geodesics are straight lines. Rapcsak considered the following problem: Given a path with the spray coefficients, find the Finsler spaces whose geodesics are the given paths. He proved a lemma (Rapcsak's lemma) giving the condition that the two Finsler metrics on the same manifold M are pointwisely projective related to each other. G. Hamel found the condition that a Finsler metric \(F=F (x, y)\) is projectively flat. This condition is given by some partial differential equations of the Finsler metric \(F\) on some open domain. The authors find some solutions to Hamel's partial differential equations that characterize the projectively flat Finsler metrics. Further, they find that some of these metrics actually have zero flag curvature. Randers metrics and the deformation of Randers metrics have an important role in this paper.
reviewed by: Hideo Shimada
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 5118302
zbMATH Keywords: Randers metric
zbMATH Keywords: Finsler metric
zbMATH Keywords: projectively flat metric
MaRDI profile type: Publication
full work available at URL: s11425-006-0703-7
OpenAlex ID: W1873807168
cites work: Projectively flat Finsler metrics of constant flag curvature
cites work: ON THE FLAG CURVATURE OF FINSLER METRICS OF SCALAR CURVATURE
cites work: Projectively flat Randers metrics with constant flag curvature
cites work: Q4445995
DOI: 10.1007/S11425-006-0703-7
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description: scientific article; zbMATH DE number 5118302