Finsler metrics of nonzero sectional flag curvature

Nonreversible Finsler Metrics of Positive Flag Curvature

Finsler metrics of scalar flag curvature and projective invariants

In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.

Randers Metrics of Sectional Flag Curvature

A Finsler metric is of sectional flag curvature if its flag curvature depends only on the section. In this article, we characterize Randers metrics of sectional flag curvature. It is proved that any non-Riemannian Randers metric of sectional flag curvature must have constant flag curvature if the dimension is greater than two. 0. Introduction Finsler geometry has a long history dated from B. Ri...

Reversible Homogeneous Finsler Metrics with Positive Flag Curvature

In this work, we continue with the classification for positively curved homogeneous Finsler spaces (G/H,F ). With the assumption that the homogeneous space G/H is odd dimensional and the positively curved metric F is reversible, we only need to consider the most difficult case left, i.e. when the isotropy group H is regular in G. Applying the fixed point set technique and the homogeneous flag c...

Some Rigidity Theorems for Finsler Manifolds of Sectional Flag Curvature

In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.