Wind Riemannian spaceforms and Randers–Kropina metrics of constant flag curvature

Randers Metrics of Scalar Flag Curvature

We study an important class of Finsler metrics — Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.

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...

Nonreversible Finsler Metrics of Positive Flag Curvature

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...

Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability

In the present paper, the nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. These results were announced in our previous paper [1]. For the flat pencils of metrics the corresponding statements and proofs were presented in the ...