Projective Ricci flat spherically symmetric Finsler metrics

In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we characterize projective Ricci flat spherically symmetric Finsler metrics. Under a certain condition, we prove that a projective Ricci flat spherically symmetric Finsler metric must be a Douglas metric. Moreover, we construct a class of new nontrivial examples on projective Ricci flat Finsler metrics.

On general (α, β)-metrics with vanishing Douglas curvature

In this paper, we study a class of Finsler metrics called general (α, β)-metrics, which are defined by a Riemannian metric α and a 1-form β. We find an equation which is necessary and sufficient condition for such Finsler metric to be a Douglas metric. By solving this equation, we obtain all of general (α, β)-metrics with vanishing Douglas curvature under certain condition. Many new non-trivial examples are explicitly constructed.

Homogeneous (α,β)-metrics of Douglas type

In this paper, we consider two related problems concerning homogeneous (α,β)-metrics. In the first part we consider homogeneous (α,β)-spaces of Douglas type. We prove that a homogeneous (α,β)-metric is a Douglas metric if and only if either