Branching laws for discrete series of some affine symmetric spaces

In this paper we study branching laws for certain unitary representations. This is done on the smooth vectors via a version of {\it period integrals}, studied in number theory, and also closely connected to symmetry-breaking operators}, introduced by T.~Kobayashi. We exhibit non-vanishing symmetry breaking operators restriction representation $\Pi$ discrete spectrum real hyperboloids representations smaller orthogonal groups. last part discuss some conjectures Arthur packets containing corresponding Arthur-Vogan groups; these are inspired Gross-Prasad conjectures.