Invariant surfaces in $\widetilde{PSL}$ 2(ℝ, τ) and applications

Abstract

We study the geometric behavior of constant mean curvature surfaces invariant by one-parameter group of isometries immersed in \(\widetilde{PSL}\)2(ℝ, τ). We give explicit examples of such surfaces. Also we give a half-space theorem for H = 1/2-rotational surfaces.