Journal of the Mathematical Society of Japan

A filtration for isoparametric hypersurfaces in Riemannian manifolds

Jianquan GE, Zizhou TANG, and Wenjiao YAN

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This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,\dots,n$. 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.

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J. Math. Soc. Japan, Volume 67, Number 3 (2015), 1179-1212.

First available in Project Euclid: 5 August 2015

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Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C24: Rigidity results

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


GE, Jianquan; TANG, Zizhou; YAN, Wenjiao. A filtration for isoparametric hypersurfaces in Riemannian manifolds. J. Math. Soc. Japan 67 (2015), no. 3, 1179--1212. doi:10.2969/jmsj/06731179.

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