Some classes of projectively and dually flat Finsler spaces with Randers change

TL;DR

This paper investigates how Randers changes affect special (l, eta)-metrics in Finsler geometry, deriving conditions for projective and dual flatness, and providing formulas for fundamental tensors and their inverses.

Contribution

It introduces formulas for fundamental and Cartan tensors of Randers-changed (l, eta)-metrics and establishes conditions for their projective and dual flatness.

Findings

Derived formulas for fundamental and Cartan tensors.

Established inverse formulas for fundamental metric tensors.

Identified conditions for projective and dual flatness.

Abstract

In this paper, we consider Randers change of some special $ (\alpha, \beta)- $ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $ (\alpha, \beta)- $metrics. Next, we establish a general formula for inverse of fundamental metric tensors of these metrics. Finally, we find the necessary and sufficient conditions under which the Randers change of these $ (\alpha, \beta)- $ metrics are projectively and locally dually flat.