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

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

2011-10-17

arxiv.org/abs/1110.3557v2

Mathematics

Differential Geometry

8 pages, to appear in Annals of Global Analysis and Geometry

Scientific paper

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.

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