On a projective class of Finsler metrics with orthogonal invariance

In this paper, we study a class of Finsler metrics, called generalized Douglas-Weyl (GDW) metrics, which includes Douglas metrics and Weyl metrics. We find a sufficient and necessary condition for an orthogonally invariant Finsler metric to be a GDW-metric. As its application, we show that a certain class of Finsler metrics with orthogonal invariance are Douglas metrics if they are GDW-metrics, generalized a theorem previously only known in the case of Weyl metrics.