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.b160551
Published 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
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