A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

Jianquan Ge; Zizhou Tang; Wenjiao Yan

A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

Differential Geometry 2013-12-19 v2

Authors: Jianquan Ge , Zizhou Tang , Wenjiao Yan

Abstract

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.

Keywords

isoparametric hypersurface Riemannian manifold classification of homogeneous hypersurfaces complex projective space complex hyperbolic space locally rank one symmetric space

Cite

@article{arxiv.1102.1126,
  title  = {A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds},
  author = {Jianquan Ge and Zizhou Tang and Wenjiao Yan},
  journal= {arXiv preprint arXiv:1102.1126},
  year   = {2013}
}

Comments

35 pages, to appear in J. Math. Soc. Jpn

A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

Abstract

Keywords

Cite

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