Homogeneous Finsler spaces with special (α, β)-metric

Document Type : Original Article

Authors
Hafez Majd
Dariush Latifi
Milad Zeinali Laki
Department of Mathematics, University of Mohaghegh Ardabili, P.O.Box. 5619911367, Ardabil-Iran.
10.22034/maco.5.2.2
Abstract
Finsler geometry is just Riemannian geometry without the quadratic restriction. In Riemannian geometry, the restriction of the metric to a tangent space
is an inner product and hence tangent spaces at different points are linearly
isometric to each other.
In this paper, we consider the special (α, β)-metric such that it is satisfying
F (α, β) = β + aα + βα2 , a ∈ R. We have investigate the geometric properties of this metric in
homogeneous spaces. We investigate the existence of invariant vector fields. Also, we obtain
the explicit formula for the S-curvature and mean Berwald curvature of homogeneous Finsler
space with this (α, β)-metric. Geodesics and geodesic vectors are other topics that we study
for these spaces.

Keywords

Subjects

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Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025