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 On a class of locally projectively flat general $(\alpha,\beta)$-metrics Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1293-1307 https://doi.org/10.4134/BKMS.b160551Published online July 31, 2017 Xiaohuan Mo and Hongmei Zhu Peking University, Henan Normal University Abstract : General $(\alpha,\beta)$-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general $(\alpha,\beta)$-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics. Keywords : Finsler metric, general $(\alpha,\beta)$ type, locally projectively flat, flag curvature MSC numbers : 53B40, 53C60 Downloads: Full-text PDF