Open Access
July, 2015 A filtration for isoparametric hypersurfaces in Riemannian manifolds
Jianquan GE, Zizhou TANG, Wenjiao YAN
J. Math. Soc. Japan 67(3): 1179-1212 (July, 2015). DOI: 10.2969/jmsj/06731179


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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Jianquan GE. Zizhou TANG. Wenjiao YAN. "A filtration for isoparametric hypersurfaces in Riemannian manifolds." J. Math. Soc. Japan 67 (3) 1179 - 1212, July, 2015.


Published: July, 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1331.53086
MathSciNet: MR3376584
Digital Object Identifier: 10.2969/jmsj/06731179

Primary: 53C24 , 53C42

Keywords: Chern Conjecture , constant mean curvature , isoparametric hypersurface , rank one symmetric space , Riccati equation

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 3 • July, 2015
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