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

Abstract

This paper is a continuation of a paper with the same title of the last two authors. In the first part of the present paper, we give a unified geometric proof that both focal submanifolds of every isoparametric hypersurface in spheres with four distinct principal curvatures are Willmore. In the second part, we completely determine which focal submanifolds are Einstein except one case.

arXiv comment19 pages,to appear in Annals of Global Analysis and Geometry

References in corpus (2)

• Isoparametric hypersurfaces with four principal curvatures, IV
• Geometry of isoparametric hypersurfaces in Riemannian manifolds

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• Isoparametric theory and its applications
• Topology and curvature of isoparametric families in spheres
• Isoparametric foliation and a problem of Besse on generalizations of Einstein condition
• Normal scalar curvature inequality on the focal submanifolds of isoparametric hypersurfaces
• Willmore submanifolds in the unit sphere via isoparametric functions
• Extrinsic geometry of the Gromoll-Meyer sphere
• On focal submanifolds of isoparametric hypersurfaces and Simons formula
• Isoparametric foliation and Yau conjecture on the first eigenvalue, II