The Relation Between Automorphism Group and Isometry Group of Randers Lie Groups

TL;DR

This paper explores the relationship between automorphism and isometry groups of simply connected Lie groups with left invariant Randers metrics, revealing conditions under which their intersection forms a maximal compact subgroup.

Contribution

It establishes a connection between automorphism and isometry groups of Randers Lie groups and identifies conditions for their intersection to be a maximal compact subgroup.

Findings

Intersection of automorphism and isometry groups can be a maximal compact subgroup.

Existence of Randers metrics with specific symmetry properties.

Special case where the intersection is maximally symmetric.

Abstract

In this paper we consider simply connected Lie groups equipped with left invariant Randers metrics which arise from left invariant Riemannian metrics and left invariant vector fields. Then we study the intersection between automorphism and isometry groups of these spaces. Finally it has shown that for any left invariant vector field, in a special case, the Lie group admits a left invariant Randers metric such that this intersection is a maximal compact subgroup of the group of automorphisms with respect to which the considered vector field is invariant.