On Projectively Flat Finsler Spaces with $(alpha, beta)$-Metric
Commun. Korean Math. Soc. 1999 Vol. 14, No. 2, 373-383
Hong-Suh Park, Il-Yong Lee
Yeungnam University, Kyungsung University
Abstract : The $(\alpha,\beta)$-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\beta$; it has been sometimes treated in theoretical physics. The condition for a Finsler space with an $(\alpha,\beta)$-metric $L(\alpha,\beta)$ to be projectively flat was given by Matsumoto [11]. The present paper is devoted to studying the condition for a Finsler space with $L=\alpha^{1-r(x)}\beta^{r(x)}$ or $L=\alpha+\beta^2/\alpha$ to be projectively flat on the basis of Matsumoto's results.
Keywords : Berwald connection, special Kropina metric, Finsler space, projectively flat
MSC numbers : 53B40
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