Invariant surfaces in Sol$_3$ with constant mean curvature and their computer graphics

TL;DR

This paper explores invariant constant mean curvature surfaces in Sol3 space, analyzing their geometric properties through computer graphics, and constructs explicit examples including minimal surfaces and spheres with constant mean curvature.

Contribution

It provides a detailed study of invariant CMC surfaces in Sol3 space, including explicit constructions and visualizations, linking them to known spheres with constant mean curvature.

Findings

Explicit examples of minimal surfaces in Sol3 space

Visualization of geometric properties via computer graphics

Relation between invariant surfaces and spheres with constant mean curvature

Abstract

In Sol$_3$ space there are three uniparametric groups of isometries. In this work we study constant mean curvature surfaces invariant by one of these groups. We analyze the geometric properties of these surfaces by means of their computer graphics. We construct explicit examples of minimal surfaces and we shall relate them with recent examples of spheres with constant mean curvature.