International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3471-3478
doi:10.1155/IJMMS.2005.3471

On Riemannian manifolds endowed with a locally conformal cosymplectic structure

Ion Mihai,1 Radu Rosca,2 and Valentin Ghişoiu1

1Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei street, Bucharest 010014, Romania
259 Avenue Emile Zola, Paris 75015, France

Received 18 September 2004; Revised 7 September 2005

Copyright © 2005 Ion Mihai et al. 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 locally conformal cosymplectic manifold M(φ,Ω,ξ,η,g) admitting a conformal contact quasi-torse-forming vector field T. The presymplectic 2-form Ω is a locally conformal cosymplectic 2-form. It is shown that T is a 3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated. The Gauss map of the hypersurface Mξ normal to ξ is conformal and Mξ×Mξ is a Chen submanifold of M×M.