Minimal translation surfaces in $So{l}_3$

Abstract

In the homogeneous space Sol${}_3$, a translation surface is parameterized by $x(s,t)=\alpha (s)\ast \beta (t)$, where $\alpha$ and $\beta$ are curves contained in coordinate planes and $\ast$ denotes the group operation of Sol${}_3$. In this paper we study translation surfaces in Sol${}_3$ whose mean curvature vanishes.

18 pages