Complete Constant Mean Curvature surfaces in homogeneous spaces

TL;DR

This paper classifies complete constant mean curvature surfaces in certain homogeneous spaces, focusing on those with Gaussian curvature of constant sign, expanding understanding of their geometric properties.

Contribution

It provides a classification of such surfaces in simply connected homogeneous manifolds with a 4-dimensional isometry group, a new result in differential geometry.

Findings

Complete CMC surfaces with non-changing Gaussian curvature sign classified

New geometric structures identified in homogeneous spaces

Advances understanding of surface behavior in these manifolds

Abstract

In this paper we classify complete surfaces of constant mean curvature whose Gaussian curvature does not change sign in a simply connected homogeneous manifold with a 4-dimensional isometry group.