A local classification of a class of \((\alpha ,\beta )\) metrics with constant flag curvature
type: Item
instance of: scholarly article
title: A local classification of a class of \((\alpha ,\beta )\) metrics with constant flag curvature
zbMATH Open document ID: 1192.53024
author: Linfeng Zhou
published in: Differential Geometry and its Applications
publication date: 2010-03-29T00:00:00Z
review text: In Finsler geometry, flag curvature represents a generalization of the notion of sectional curvature from Riemannian geometry. This paper completes the local classification of (\(\alpha , \beta \)) metrics of the type \(F=\alpha(1+{{\beta}\over{\alpha}})^2 \), with constant flag curvature. The author proves that if such a metric has constant flag curvature, then the Finsler space must be locally projectively flat. Then, he studies another class of (\(\alpha , \beta \)) metrics with \(F=\alpha(1+{{\beta}\over{\alpha}})^p, |{p}|>1 \). He obtains that there are no non-trivial Matsumoto metrics (called a slope of the mountain) with constant flag curvature.
reviewed by: Oana Constantinescu
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 5687512
zbMATH Keywords: (\(\alpha,\beta \)) metrics
zbMATH Keywords: locally projectively flat
Wikidata QID: Q115357216
MaRDI profile type: Publication
full work available at URL: j.difgeo.2009.05.008
OpenAlex ID: W2007561010
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DOI: 10.1016/J.DIFGEO.2009.05.008
description: scientific article; zbMATH DE number 5687512