ON A CLASS OF SINGULAR PROJECTIVELY FLAT FINSLER METRICS WITH CONSTANT FLAG CURVATURE

Projectively Flat Finsler Metrics of Constant Curvature

It is the Hilbert’s Fourth Problem to characterize the (not-necessarilyreversible) distance functions on a bounded convex domain in R such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scala...

On a class of locally projectively flat Finsler metrics

‎In this paper we study Finsler metrics with orthogonal invariance‎. ‎We‎ ‎find a partial differential equation equivalent to these metrics being locally projectively flat‎. ‎Some applications are given‎. ‎In particular‎, ‎we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.

on a class of locally dually flat finsler metrics with isotropic s-curvature

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

Nonreversible Finsler Metrics of Positive Flag Curvature

On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics

We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of t...