Cylinders as Left Invariant CMC Surfaces in ${\mathrm{Sol}}_3$ and $E(\kappa ,\tau )$-Spaces Diffeomorphic to ${\mathbb{R}}^3$

Miroslav Vržina

In the present paper we give a geometric proof for the existence of cylinders with constant mean curvature $H>H(X)$ in certain simply connected homogeneous three-manifolds $X$ diff…