Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes
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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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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s12220-016-9686-y
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Díaz-Ramos, J.C., Domínguez-Vázquez, M. & Vidal-Castiñeira, C. Real Hypersurfaces with Two Principal Curvatures in Complex Projective and Hyperbolic Planes. J Geom Anal 27, 442–465 (2017). https://doi.org/10.1007/s12220-016-9686-y