Rotational and Parabolic Surfaces in PSL2(R,tau) and Applications

TL;DR

This paper investigates constant mean curvature surfaces invariant under specific isometries within the homogeneous manifold PSL2(R,tau), providing new insights and applications in differential geometry.

Contribution

It introduces a classification of such surfaces in PSL2(R,tau) and explores their applications, extending previous work on invariant surfaces in homogeneous spaces.

Findings

Classification of rotational invariant CMC surfaces in PSL2(R,tau)

Analysis of parabolic invariant CMC surfaces

Applications to geometric problems in homogeneous manifolds

Abstract

We study surfaces of constant mean curvature which are invariant by oneparameter group of either rotational isometries or parabolic isometries, immersed into the homogeneous manifold PSL2(R,tau). Also, we give some applications.