Projectively Flat Finsler Space with A \(r\)-th Series \((\alpha,\beta)\)-Metric

Aveesh S.T., S.K. Narasimhamurthy, G. Ramesh


The \((\alpha,\beta)\)-metric is a Finsler metric which is constructed from a Riemannian metric 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. The present paper, We discuss the \(r\)-th series \((\alpha, \beta)\)-metric to be projectively flat on the basis of Matsumoto's results.


Finsler space; $r$-th series $(\alpha,\beta)$-metric; Projectively flat

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