On m-th root Finsler metrics

Abstract

In this paper, we characterize locally dually flat and Antonelli m-th root Finsler metrics. Then, we show that every m-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.

Some properties of m-th root Finsler metrics

“…A Finsler metric F = F (x, y) on a manifold M is said to be locally dually flat if at any point there is a coordinate system (x i ) in which the spray coefficients are in the following form y) for all λ > 0. Such a coordinate system is called an adapted coordinate system [15]. Recently, Shen proved that the Finsler metric F on an open subset U ⊂ R n is dually flat if and only if it satisfies…”

On m-th root metrics with special curvature properties

“…You show that an m-th root Einstein Finsler metric is Ricci-flat [9]. The authors characterize locally dually flat m-th root Finsler metrics as well as m-th root y-Berwald metrics in [8].…”

A new class of projectively flat Finsler metrics with constant flag curvatureK=1

“…In [18], Tayebi-Najafi characterize locally dually flat and Antonelli m-th root Finsler metrics. In [19], they prove that every m-th root Finsler metric of isotropic Landsberg metric reduces to a Landsberg metric.…”