English

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