Curvature-adapted submanifolds of symmetric spaces

Details Curvature-adapted submanifolds of symmetric spaces Curvature-adapted submanifolds of symmetric spaces

2011-02-23

arxiv.org/abs/1102.4756v2

Mathematics

Differential Geometry

Theorem 1.4 strengthened from previous version. To appear in Indiana. U. Math. J

Scientific paper

We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any compact symmetric space. Our second objective is to investigate such hypersurfaces in some specific symmetric spaces. Various classification results in the Cayley projective and hyperbolic planes and in complex two-plane Grassmannians are obtained under some additional assumptions.

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