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