Reversible homogeneous Finsler metrics with positive flag curvature

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...

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.

Geodesic behavior for Finsler metrics of constant positive flag curvature on S

We study non-reversible Finsler metrics with constant flag curvature 1 on S and show that the geodesic flow of every such metric is conjugate to that of one of Katok’s examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metrics with c...

Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...