Almost conformal 2-cosymplectic pseudo-Sasakian manifolds

Abstract

In the last years several papers have been concerned with almost r-contact or r-paracontact manifolds (see [6] and [14]). On the other hand, V.V. Goldberg and R. Rosta have recently studied in [12] almost 1-contact pseudo-Riemannian manifolds which are endowed with a conformal cosymplectic pseudo-Sasakian structure. Since the manifolds M which we are going to discuss are connected and paracompact,we denote by : exterior product by the closed 1-form ) the cohomology operator (see [13]) on M. Then any form such that is said to be -closed. The present paper is devoted to the study of even dimensional pseudo Riemannian manifolds of signature which are endowed with an almost conformal 2-cosymplectic pseudo-Sasakian structure. Such a manifold is denoted by , and its structure tensor fields are: the paracomplex operator (see [15]), an exterior recurrent (see [9]) 2-form of rank , two structure vector fields , two structure 1-forms is the musical isomorphism [6] defined by g ) and the pseudo-Riemannian tensor g of M respectively.