Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes

Abstract

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian flat surfaces with parallel mean curvature or, equivalently, by principal orbits of a cohomogeneity two polar action.

References in corpus (1)

• Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms

Cited by in corpus (1)

• Hypersurfaces in $C{P}^2$ and $C{H}^2$ with two distinct principal curvatures