Ruled hypersurfaces with constant mean curvature in complex space forms

TL;DR

This paper classifies ruled real hypersurfaces with constant mean curvature in complex space forms, showing they must be minimal, thus providing a complete classification based on existing results.

Contribution

It proves that such hypersurfaces are necessarily minimal, extending the classification of ruled real hypersurfaces in complex space forms.

Findings

Ruled real hypersurfaces with constant mean curvature are minimal.

Complete classification of these hypersurfaces in complex projective and hyperbolic spaces.

Utilizes existing results to establish minimality and classification.

Abstract

We show that ruled real hypersurfaces with constant mean curvature in the complex projective and hyperbolic spaces must be minimal. This provides their classification, by virtue of a result of Lohnherr and Reckziegel.