A filtration for isoparametric hypersurfaces in Riemannian manifolds

Jianquan Ge; Zizhou Tang; Wenjiao Yan

doi:10.2969/jmsj/06731179

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

A filtration for isoparametric hypersurfaces in Riemannian manifolds

Jianquan Ge, Zizhou Tang, Wenjiao Yan

著者情報

キーワード: isoparametric hypersurface, constant mean curvature, rank one symmetric space, Riccati equation, Chern conjecture

ジャーナルフリー

2015 年 67 巻 3 号 p. 1179-1212

DOI https://doi.org/10.2969/jmsj/06731179

詳細

抄録

This paper introduces the notion of k-isoparametric hypersurface in an (n+1)-dimensional Riemannian manifold for k = 0,1,…,n. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among other things) are given in complex projective spaces, complex hyperbolic spaces, and even in locally rank one symmetric spaces.