The classification of ϕ-symmetric Sasakian manifolds

A φ{symbol}-symmetric space M is a complete connected regular Sasakian manifold, that fibers over an Hermitian symmetric space N, so that the geodesic involutions of N lift to define global (involutive) automorphisms of the Sasakian structure on M. In the present paper the complete classification of φ{symbol}-symmetric spaces is obtained. The groups of automorphisms of the Sasakian structures and the groups of isometries of the underlying Riemannian metrics are determined. As a corollary, the Sasakian space forms are also determined.