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

Abstract

An isometric immersion $x:M^n\to S^{n+p}$ is called Willmore if it is an extremal submanifold of the Willmore functional: $W(x)={\int }_{M^n}(S-n{H}^2{)}^{\frac{n}{2}}dv$, 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.

arXiv comment8 pages, to appear in Annals of Global Analysis and Geometry