Contact hypersurfaces in Kaehler manifolds

A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric SO(n+2)/SO(n)SO(2) and its noncompact dual space SO(n,2)/SO(n)SO(2) for n > 2.