On a Class of Finsler Metrics of Douglas Type

Abstract

In this paper, we study a class of Finsler metrics of cohomogeneity two on ℝ × ℝⁿ. They are called weakly orthogonally invariant Finsler metrics. These metrics not only contain spherically symmetric Finsler metrics and Marcal–Shen’s warped product metrics but also partly contain another “warping” introduced by Chen–Shen–Zhao. We obtain differential equations that characterize weakly orthogonally invariant Finsler metrics with vanishing Douglas curvature, and therefore we provide a unifying frame work for Douglas equations due to Liu–Mo, Mo–Solórzano–Tenenblat and Solórzano. As an application, we obtain a lot of new examples of weakly orthogonally invariant Douglas metrics.