Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space

TL;DR

This paper classifies ruled real hypersurfaces with a constant norm shape operator in complex space forms, establishing the existence of a unique inhomogeneous example in complex hyperbolic space.

Contribution

It completes the classification by proving the existence of a unique inhomogeneous example in complex hyperbolic space.

Findings

Existence of a unique inhomogeneous hypersurface in complex hyperbolic space.

Classification of ruled real hypersurfaces with constant shape operator norm.

Extension of previous classifications in complex space forms.

Abstract

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.