New examples of Willmore submanifolds in the unit sphere via isoparametric functions

TL;DR

This paper introduces new examples of Willmore submanifolds in the unit sphere constructed through isoparametric functions of FKM-type, expanding the limited known instances of such submanifolds.

Contribution

It provides a novel method for constructing Willmore submanifolds using isoparametric functions of FKM-type, adding to the scarce examples in the literature.

Findings

New examples of Willmore submanifolds in the unit sphere.

Construction method via isoparametric functions of FKM-type.

Expands the known class of Willmore submanifolds.

Abstract

An isometric immersion $x:M^n\rightarrow S^{n+p}$ is called Willmore if it is an extremal submanifold of the Willmore functional: $W(x)=\int_{M^n} (S-nH^2)^{\frac{n}{2}}dv$, where $S$ is the norm square of the second fundamental form and $H$ is the mean curvature. Examples of Willmore submanifolds in the unit sphere are scarce in the literature. The present paper gives a series of new examples of Willmore submanifolds in the unit sphere via isoparametric functions of FKM-type.