# 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.

## Key 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.