Projective change between two classes \(of(\alpha ,\beta )\)-metrics
type: Item
instance of: scholarly article
title: Projective change between two classes \(of(\alpha ,\beta )\)-metrics
zbMATH Open document ID: 1176.53034
published in: Differential Geometry and its Applications
publication date: 2009-08-21T00:00:00Z
review text: Within the framework of Finsler geometry, the paper determines for dimension \(n\geq3\) \ the equations which characterize the projective change between the \((\alpha,\beta)-\)metric \(F=(\alpha+\beta)^2/\alpha\) and the Randers metric \({\bar F}={\bar \alpha}+{\bar \beta}\), where \(\alpha\) and \({\bar\alpha}\) are Riemannian metrics and \(\beta,{\bar \beta}\) are nonzero one forms. This result extends another one obtained in [\textit{Z. Shen, G. Civi Yildirim}, Can. J. Math. 60, No. 2, 443--456 (2008; Zbl 1157.53014)]. As well, the projective change is studied in the case when \(F\) satisfies certain curvature properties.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 5597825
zbMATH Keywords: Finsler manifold
zbMATH Keywords: projective change
zbMATH Keywords: Randers metric
zbMATH Keywords: the Douglas tensor.
author: Ningwei Cui
author: Yi-Bing Shen
MaRDI profile type: Publication
full work available at URL: j.difgeo.2009.03.003
OpenAlex ID: W2081396098
Wikidata QID: Q115357295
cites work: Q4847037
cites work: Q3446384
cites work: Q3915585
cites work: Q4324068
cites work: Q3284349
cites work: ON PROJECTIVELY RELATED RANDERS METRICS
cites work: Differential geometry of spray and Finsler spaces
cites work: On a Class of Projectively Flat Metrics with Constant Flag Curvature
cites work: On invariant tensors of \(\beta\)-changes of Finsler metrics
DOI: 10.1016/J.DIFGEO.2009.03.003
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description: scientific article; zbMATH DE number 5597825