A filtration for isoparametric hypersurfaces in Riemannian manifolds

作者：Ge, Jianquan^*; Tang, Zizhou; Yan, Wenjiao

来源：Journal of the Mathematical Society of Japan, 2015, 67(3): 1179-1212.

DOI：10.2969/jmsj/06731179

• isoparametric hypersurface
• constant mean curvature
• rank one symmetric space
• Riccati equation
• Chern conjecture

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.

• 出版日期2015-7
• 单位北京师范大学