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Projectively flat Finsler space with an approximate Matsumoto metric. (English) Zbl 1101.53301

Summary: The Matsumoto metric is an \((\alpha,\beta)\)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for \(|\beta|<|\alpha|\) by the first author. He introduced an approximate Matsumoto metric as the \((\alpha,\beta)\)-metric of finite series form and investigated by Park, Hong-Suh; Lee, Il-Yong; Park, Chan Keun in [Indian J. Pure Appl. Math. 34, No.1, 59-77 (2003; Zbl 1030.53025)]. The purpose of the present paperis devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)

Citations:

Zbl 1030.53025
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