Minimal Surfaces in $S^3$ with Constant Contact Angle

TL;DR

This paper characterizes the Clifford Torus in S3 as the unique minimal surface with constant contact angle, using moving frames and contact structure equations, and discusses applications and examples.

Contribution

It provides a novel characterization of the Clifford Torus in S3 based on contact angle conditions, expanding understanding of minimal surfaces in spherical geometry.

Findings

Clifford Torus uniquely characterized by constant contact angle

Minimal surfaces with constant contact angle in S3 are Clifford Tori

Applications and examples illustrating the characterization

Abstract

We provide a characterization of the Clifford Torus in S3 via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S3 with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.