Curvature-adapted submanifolds of symmetric spaces
Differential Geometry
2012-02-21 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1102.4756,
title = {Curvature-adapted submanifolds of symmetric spaces},
author = {Thomas Murphy},
journal= {arXiv preprint arXiv:1102.4756},
year = {2012}
}
Comments
Theorem 1.4 strengthened from previous version. To appear in Indiana. U. Math. J