2013•arXiv (Cornell University)Open access

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

José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Cristina Vidal-Castiñeira

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.

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Key concepts: Principal curvature, Hypersurface, Mathematics, Equidistant, Curvature, Principal (computer security), Mathematical analysis, Pure mathematics