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

Copyright © 2004 Adela Mihai and Radu Rosca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.