On the geometry of null hypersurfaces of indefinite complex contact manifolds

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 $-3$.