A class of Finsler metrics with isotropic S-curvature

Abstract

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We characterize these metrics with isotropic S-curvature.

On a Class of Finsler Metrics With Isotropic Berwald Curvature

“…Finally, it is worth mentioning that the S-curvature is an important nonRiemannian quantity in Finsler geometry [4,7,16]. It interacts with the flag curvature in a mysterious way.…”

“…It interacts with the flag curvature in a mysterious way. Recently, Cheng-Shen have characterized (α, β)-metrics with isotropic S-curvature [7].…”

“…S(x, y) is called the S-curvature [7,9,16]. F is said to have isotropic S-curvature if there is a scalar function κ(x) on M such that (2.5)…”

On Curvatures of Homogeneous Finsler Space with Special (𝜶, 𝜷)-Metric

“…, )) be the local coordinate system. With reference to [5], to find the S-curvature in local coordinate system, we need to evaluate the following quantities at the origin:…”

Locally dually flat Finsler (�,�)-metric

“…The concept of , − was introduced in 1972 by M. Matsumoto and studied by many authors like ( [4], [5], [9], [6], [10], [2]). The …”