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

摘要

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