Contact hypersurfaces in Kähler manifolds

A contact hypersurface in a Kähler 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 Kähler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric $Q^n = SO_{n+2}/SO_nSO_2$ and its noncompact dual space $Q^{n*} = SO^o_{n,2}/SO_nSO_2$ for $n \geq 3$.