Isoparametric foliation and a problem of Besse on generalizations of Einstein condition

Abstract

The focal sets of isoparametric hypersurfaces in spheres with g = 4 are all Willmore submanifolds, being minimal but mostly non-Einstein ([TY1], [QTY]). Inspired by A.Gray's view, the present paper shows that, these focal sets are all A- manifolds but rarely Ricci parallel, except possibly for the only unclassified case. As a byproduct, it gives infinitely many simply-connected examples to the problem 16.56 (i) of Besse concerning generalizations of the Einstein condition.

To appear in Advances in Mathematics

References in corpus (2)

• New examples of Willmore submanifolds in the unit sphere via isoparametric functions,II
• On A-tensors in Riemannian geometry

Cited by in corpus (2)

• Willmore submanifolds in the unit sphere via isoparametric functions
• On focal submanifolds of isoparametric hypersurfaces and Simons formula