^{1}Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China.

^{2}College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China.

Receive Date: 02 September 2015,
Revise Date: 29 January 2016,
Accept Date: 29 January 2016

Abstract

In this paper we study Finsler metrics with orthogonal invariance. We find a partial differential equation equivalent to these metrics being locally projectively flat. Some applications are given. In particular, we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.

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