On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature

In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these metrics by warped product. Using the obtained equations, we manufacture new locally projectively flat Finsler warped product metrics of vanishing flag curvature. These metrics contain the metric introduced by Berwald and the spherically symmetric metric given by Mo-Zhu.

On almost contact Finsler structures

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

New classes of projectively related Finsler metrics of constant flag curvature

We define a Weyl-type curvature tensor of [Formula: see text]-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect, we construct new families of projectively related Finsler metrics that have constant flag curvature.

The geometry of a positively curved Zoll surface of revolution

In this paper, we study the geometry of the manifolds of geodesics of a Zoll surface of positive Gauss curvature, show how these metrics induce Finsler metrics of constant flag curvature and give some explicit constructions.

Some eigenvalue comparison theorems of Finsler p-Laplacian

We obtain Cheng type inequality, Cheeger type inequality, Faber–Krahn type inequality and McKean type inequality of [Formula: see text]-Laplacian on a Finsler manifold. These generalize the corresponding theorems in Riemannian geometry and sharpen some results in recent literatures. Moreover, for a complete noncompact Finsler manifold with negative constant flag curvature and vanishing [Formula: see text] curvature, the first eigenvalue is calculated.