Some minimal submanifolds generalizing the Clifford torus

TL;DR

This paper explores a class of minimal submanifolds in spheres that extend the properties of the Clifford torus, such as being product surfaces and helicoidal, revealing broader geometric structures.

Contribution

It introduces new minimal submanifolds in spheres that generalize the Clifford torus's properties, expanding understanding of minimal surface geometry.

Findings

Identification of new minimal submanifolds with product and helicoidal properties

Generalization of the Clifford torus in higher-dimensional spheres

Enhanced understanding of minimal surface structures in spherical geometry

Abstract

The Clifford torus is a product surface in $\mathbb S^3$ and it is helicoidal. It will be shown that more minimal submanifolds of $\mathbb S^n$ have these properties.