On Finsler Σ-spaces

Abstract

Listen

Translate article

In this paper, we study Finsler Σ-spaces. We first prove that any Σ-space is a homogeneous Finsler space. Then we study some geometric properties of Berwald Σ-spaces and prove that any generalized symmetric Berwald space is a Berwald Σ-space where Σ is cyclic. Then we show that if each Sσ is parallel with respect to Berwald connection of a Berwald Σ-space then the space is locally symmetric. Finally we study some existence theorems.