International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 10, Pages 535-540
doi:10.1155/S0161171204307143

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

Adela Mihai1 and Radu Rosca2

 1Department of Geometry, Faculty of Mathematics, University of Bucharest, Street Academiei 14, Bucharest 70109, Romania
259 avenue Emile Zola, Paris 75015, France
Received 16 July 2003

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.