Weinstein's theorem for Finsler manifolds
type: Item
instance of: scholarly article
title: Weinstein's theorem for Finsler manifolds
zbMATH Open document ID: 1178.53077
author: László Kozma
author: Ioan Radu Peter
published in: Journal of Mathematics of Kyoto University
publication date: 2007-02-20T00:00:00Z
review text: An isometry of a Finsler manifold is a diffeomorphism \(f: M\to M \) which preserves the distance. Equivalently, \(f\) preserves the Finsler norms of the tangent vectors cf. [\textit{S. Deng} and \textit{Z. Hou}, Pac. J. Math. 207, No.~1, 149--155 (2002; Zbl 1055.53055)]. The authors prove Weinstein's Theorem for Finsler manifolds: Let \(f\) be an isometry of a compact oriented positively homogeneous Finsler manifold \(M\) of dimension \(n\). If \(M\) has positive flag curvature and \(f\) preserves the orientation of \(M\) for \(n\) even and reverses the orientation of \(M\) for \(n\) odd, then, \(f\) has a fixed point. The proof is very detailed, based on results from the Finslerian geometry, on the line of Weinstein's proof.
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 5128994
zbMATH Keywords: Finsler manifolds
zbMATH Keywords: isometries
zbMATH Keywords: fixed points
zbMATH Keywords: flag curvature
reviewed by: Mihai Anastasiei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250281783
OpenAlex ID: W1518749497
DOI: 10.1215/KJM/1250281783
description: scientific article; zbMATH DE number 5128994