On locally dually flat \((\alpha,\beta)\)-metrics with isotropic S-curvature
type: Item
instance of: scholarly article
title: On locally dually flat \((\alpha,\beta)\)-metrics with isotropic S-curvature
zbMATH Open document ID: 1266.53024
author: E. Peyghan
author: Hassan Sadeghi
author: A. Tayebi
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2013-04-05T00:00:00Z
review text: A Finsler metric \(F(x,y)\) is said to be locally dually flat if there exists a scalar function \(H(x,y)\), such that \[ G^i=\frac 12 g^{ij}H_{y^j}. \] The authors prove that: 1) a Finsler space with an \((\alpha,\beta)\) metric \[ F(x,y)=\alpha \phi \left(\frac{\alpha}{\beta}\right),\quad \phi'(0)=\phi'''(0)=0,\quad \phi'(0)\neq 0,\quad \frac{\phi''(0)}{\phi(0)}>-1\tag{*} \] is locally dually flat with isotropic \(S\)-curvature iff it is locally Minkowskian: 2) a locally dually flat Finsler space with \((*)\) and with isotropic \(S\)-curvature is locally projectively flat.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 6150658
zbMATH Keywords: Finsler metric
zbMATH Keywords: locally dually flat
zbMATH Keywords: Minkowskian
zbMATH Keywords: \(S\)-curvature
zbMATH Keywords: projectively flat
reviewed by: Lajos Tamássy
MaRDI profile type: Publication
full work available at URL: s13226-012-0031-2
OpenAlex ID: W2082651851
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DOI: 10.1007/S13226-012-0031-2
description: scientific article; zbMATH DE number 6150658