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

Abstract

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.