Isoparametric foliation and a problem of Besse on generalizations of Einstein condition
Differential Geometry
2016-11-26 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1307.3807,
title = {Isoparametric foliation and a problem of Besse on generalizations of Einstein condition},
author = {Zizhou Tang and Wenjiao Yan},
journal= {arXiv preprint arXiv:1307.3807},
year = {2016}
}
Comments
To appear in Advances in Mathematics