On the geodesics of homogeneous Finsler spaces with some special $(\alpha, \beta)$-metrics

TL;DR

This paper investigates the properties of geodesics and geodesic vectors in specific homogeneous Finsler spaces, providing conditions for vectors to be geodesic, thus advancing understanding of these geometric structures.

Contribution

It introduces necessary and sufficient conditions for geodesic vectors in homogeneous exponential and infinite series Finsler spaces, focusing on special $(eta, eta)$-metrics.

Findings

Characterization of geodesic vectors in these spaces

Necessary and sufficient conditions for geodesic vectors

Enhanced understanding of geodesic structure in special Finsler spaces

Abstract

In this paper, we study geodesics and geodesic vectors for homogeneous exponential Finsler space and homogeneous infinite series Finsler space. Further, we find necessary and sufficient condition for a non-zero vector in these homogeneous spaces to be a geodesic vector.