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arXiv · 1110.3557

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

Zizhou Tang·Wenjiao Yan
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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.

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Zizhou Tang, Wenjiao Yan. 2012-03-19. New examples of Willmore submanifolds in the unit sphere via isoparametric functions. https://arxiv.org/abs/1110.3557

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