Park, Hong-Suh; Lee, Il-Yong; Park, Ha-Yong; Kim, Byung-Doo Projectively flat Finsler space with an approximate Matsumoto metric. (English) Zbl 1101.53301 Commun. Korean Math. Soc. 18, No. 3, 501-513 (2003). 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) Keywords:Finsler space; projectively flat; Matsumoto metric; approximate Matsumoto metric; homogeneous polynomials in \((y^i)\) of degree \(r\) Citations:Zbl 1030.53025 PDFBibTeX XMLCite \textit{H.-S. Park} et al., Commun. Korean Math. Soc. 18, No. 3, 501--513 (2003; Zbl 1101.53301) Full Text: DOI