A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

Details A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

2011-02-06

arxiv.org/abs/1102.1126v1

Mathematics

Differential Geometry

34 pages

Scientific paper

Motivated by the well known Cartan-M\"{u}nzner equations and the Chern conjecture, we introduce 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. Further investigations in this direction are expected.

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