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arXiv · 1307.3807

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

Zizhou Tang·Wenjiao Yan
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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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Zizhou Tang, Wenjiao Yan. 2013-07-15. Isoparametric foliation and a problem of Besse on generalizations of Einstein condition. https://arxiv.org/abs/1307.3807

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