On the geometry of null hypersurfaces of indefinite complex contact manifolds

TL;DR

This paper investigates the geometry of null hypersurfaces within indefinite complex contact manifolds, providing classification results and characterizations of the ambient space based on hypersurface properties.

Contribution

It offers new classification results for null hypersurfaces and characterizes the ambient space as having constant $GH$-sectional curvature under certain conditions.

Findings

Classification of null hypersurfaces including totally umbilic and screen conformal types.

Characterization of the ambient space as a space of constant $GH$-sectional curvature -3.

Proved that specific hypersurface conditions imply the ambient manifold's curvature is constant.

Abstract

We study the geometry of null hypersurfaces in indefinite complex contact manifolds. We prove several classification results for a variety of well-known null hypersurfaces, including the totally umbilic, totally screen umbilic, and the screen conformal ones. Furthermore, a characterization of the ambient space is given in case the underlying null hypersurface is totally contact umbilic, totally contact screen umbilic or contact screen conformal, i.e. we have proved that the ambient complex contact manifold must be a space of constant $GH$-sectional curvature of $-3$.