Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(4): 1293-1307

Online first article January 12, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160551

Copyright © The Korean Mathematical Society.

On a class of locally projectively flat general $(\alpha,\beta)$-metrics

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