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Isoparametric foliation and a problem of Besse on generalizations of Einstein condition (1307.3807v3)

Published 15 Jul 2013 in math.DG and math.AT

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.

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