Isometries of Almost-Riemannian structures on nonnilpotent, solvable 3D Lie groups

TL;DR

This paper proves that automorphisms are the only isometries for rank two Almost-Riemannian Structures on certain 3D Lie groups, leading to a classification of these structures.

Contribution

It establishes the uniqueness of isometries as automorphisms for rank two ARSs on nonnilpotent, solvable 3D Lie groups and classifies these structures.

Findings

Automorphisms are the only isometries for the structures.

Classification of rank two ARSs on the specified Lie groups.

Results apply to nonnilpotent, solvable 3D Lie groups.

Abstract

In this paper we prove that automorphisms are the only isometries between rank two Almost-Riemannian Structures on the class of nonnilpotent, solvable, connected 3D Lie groups. As a consequence, a classification result for rank two ARSs on the groups in question is obtained.