Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes

TL;DR

This paper characterizes specific hypersurfaces in complex projective and hyperbolic planes, providing classifications of austere and Levi-flat hypersurfaces with constant mean curvature.

Contribution

It offers a geometric characterization of cohomogeneity one hypersurfaces and partial classifications of austere and Levi-flat hypersurfaces in these spaces.

Findings

Characterization of certain cohomogeneity one hypersurfaces

Partial classification of austere hypersurfaces

Partial classification of Levi-flat hypersurfaces with constant mean curvature

Abstract

We give a geometric characterization of certain hypersurfaces of cohomogeneity one in the complex projective and hyperbolic planes. We also obtain some partial classifications of austere hypersurfaces and of Levi-flat hypersurfaces with constant mean curvature in these spaces.