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

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.