Skew-symmetric vector fields on a CR-submanifold of a para-Kählerian manifold

We deal with a CR-submanifold M of a para-Kählerian manifold M, which carries a J-skew-symmetric vector field X. It is shown that X defines a global Hamiltonian of the symplectic form Ω on M and JX is a relative infinitesimal automorphism of Ω. Other geometric properties are given. 1. Introduction. CR-submanifolds M of some pseudo-Riemannian manifolds M have been first investigated by Rosca [10], and also studied in [2, 3, 11]. If M is a para-Kählerian manifold, it has been proved that any coisotropic submani-fold M of M is a CR-submanifold (such CR-submanifolds have been denominated CICR-submanifolds [6]). In this note, one considers a foliate CICR-submanifold M of a para-Kählerian man-ifold M(J, Ω, g). It is proved that the necessary and sufficient condition in order that the leaf M of the horizontal distribution D on M carries a J-skew-symmetric vector