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 $d^ω=d+e(ω) (e(ω)$: exterior product by the closed 1-form $ω$ ) the cohomology operator (see [13]) on M. Then any form $u∈ M$ such that $d^ω u=0$ is said to be $d^ω$-closed. The present paper is devoted to the study of even dimensional pseudo Riemannian manifolds of signature $(m + 2,m)$ which are endowed with an almost conformal 2-cosymplectic pseudo-Sasakian structure. Such a manifold is denoted by $M(U, ω, \xi_?, η^?,g)$, and its structure tensor fields $(U,ω,\xi_?,η^?,g)$ are: the paracomplex operator (see [15]), an exterior recurrent (see [9]) 2-form of rank $2m$, two structure vector fields $\xi_?; ?=2m+1, 2m+2$, two structure 1-forms $η^?=\flat(\xi_?)$ $\flat: TM→ T^* M$ is the musical isomorphism [6] defined by g) and the pseudo-Riemannian tensor g of M respectively.