Almost-Riemannian Structures on nonnilpotent, solvable 3D Lie groups

TL;DR

This paper investigates Almost-Riemannian Structures on nonnilpotent, solvable 3D Lie groups, demonstrating that their singular loci are always embedded submanifolds, thus advancing understanding of geometric structures on these groups.

Contribution

It provides a detailed analysis of ARS on nonnilpotent, solvable 3D Lie groups, establishing that their singular loci are embedded submanifolds, a novel geometric insight.

Findings

Singular loci are always embedded submanifolds

ARS structures are well-behaved on these groups

Provides geometric characterization of ARS on 3D Lie groups

Abstract

In this paper we study Almost-Riemannian Structures (ARS) on the class of nonnilpotent, solvable, conneted 3D Lie groups. The nice structures present in such groups allow us to show that the singular locus of ARSs on such groups are always embedded submanifolds.