Topology and Embeddedness of Lawson's Bipolar Surfaces in the 5-Sphere

TL;DR

This paper classifies Lawson's bipolar minimal surfaces in the 5-sphere, providing bounds on their area and demonstrating that they are not embedded, advancing understanding of their topology and geometry.

Contribution

It offers a topological classification of Lawson's bipolar minimal surfaces and establishes bounds on their area, revealing their non-embedded nature.

Findings

Surfaces are not embedded.

Derived bounds on surface area.

Topological classification of bipolar surfaces.

Abstract

We give a topological classification of Lawson's bipolar minimal surfaces corresponding to his $\xi$- and $\eta$-family. Therefrom we deduce upper as well as lower bounds on the area of these surfaces, and find that they are not embedded.