Helix surfaces in the special linear group

Abstract

We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\mathring{)}$. 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 $\mathrm{SL}(2,\mathring{)}$.

Minor corrections. To appear in Annali di Matematica Pura e Applicata. arXiv admin note: substantial text overlap with arXiv:1206.1274