Helix surfaces in the special linear group

TL;DR

This paper characterizes helix surfaces in the special linear group SL(2,R), providing explicit local descriptions using curves and isometries, advancing understanding of geometric structures in this space.

Contribution

It offers a novel explicit local description of helix surfaces in SL(2,R) based on curves and isometries, enriching geometric analysis in Lie groups.

Findings

Explicit local descriptions of helix surfaces in SL(2,R)

Characterization of constant angle surfaces in the group

Use of isometries to describe surface geometry

Abstract

We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\r)$. In particular, we give an explicit local description of these surfaces in terms of a suitable curve and a 1-parameter family of isometries of $\mathrm{SL}(2,\r)$.