On projective equivalence and pointwise projective relation of Randers metrics
type: Item
instance of: scholarly article
zbMATH Open document ID: 1253.53018
DOI: 10.1142/S0129167X12500930
published in: International Journal of Mathematics
publication date: 2012-09-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1112.6143
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 6078198
zbMATH Keywords: Finsler metrics
zbMATH Keywords: Randers metrics
zbMATH Keywords: projective equivalence
zbMATH Keywords: pointwise projective relation
zbMATH Keywords: projective transformations
author: Vladimir S. Matveev
MaRDI profile type: Publication
arXiv ID: 1112.6143
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OpenAlex ID: W3099242370
title: On projective equivalence and pointwise projective relation of Randers metrics
review text: A Randers metric is a Finsler metric of the form \(F(x,\xi )=\sqrt{g_{ij}(x)\xi ^i\xi ^j}+\omega _i(x)\xi ^i\), where \(g_{ij}\) is a Riemannian metric and \(\omega _i\) is a one-form. In this paper the author proves that the projective equivalence of two Randers metrics \(F=\sqrt{g(\xi ,\xi )}+\omega (\xi )\) and \(\overline{F}=\sqrt{\overline{g}(\xi ,\xi )}+\overline{\omega }(\xi ),\) such that at least one of the one-forms \(\omega\) and \(\overline{\omega }\) is not closed, implies that for a certain constant \(C>0\) we have \(g=C^2\overline{g}\) and the form \(\omega -C\overline{\omega }\) is closed. Finally, as an application, the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics is proved.
reviewed by: Liviu Popescu
description: scientific article; zbMATH DE number 6078198