Spherical CR-symmetric hypersurfaces in Hermitian symmetric spaces

We give the realization of spherical CR-symmetric manifolds M2n+1, n≥2, as real hypersurfaces in Hermitian symmetric spaces of rank 1 or rank 2. In addition, we give a complete classification of CR-symmetric contact 3-manifolds. Using the generalized Tanaka–Webster connection, we prove classification theorems of locally pseudo-Hermitian symmetric CR space forms of higher dimension and of dimension 3.