Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group $SOLV^-$

TL;DR

This paper characterizes the geodesics of a specific sub-Riemannian metric on the three-dimensional solvable Lie group $SOLV^-$, providing insights into its geometric structure.

Contribution

It offers a detailed description of sub-Riemannian geodesics on $SOLV^-$, a less-studied solvable Lie group, expanding understanding of its geometric properties.

Findings

Explicit formulas for geodesics on $SOLV^-$

Analysis of geodesic behavior and properties

Contribution to sub-Riemannian geometry on solvable Lie groups

Abstract

In this paper we describe the geodesics of a left-invariant sub-Riemannian metric on the three-dimensional solvable Lie group $SOLV^-$.