Almost conformal 2-cosymplectic pseudo-Sasakian manifolds


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<sup>ω</sup>=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<sup>ω</sup> u=0 is said to be d<sup>ω</sup>-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_𝛼, η^𝛼,g), and its structure tensor fields (U,ω,\xi_𝛼,η^𝛼,g) are: the paracomplex operator (see [15]), an exterior recurrent (see [9]) 2-form of rank 2m, two structure vector fields \xi_𝛼; 𝛼=2m+1, 2m+2, two structure 1-forms η^𝛼=\flat(\xi_𝛼) \flat: TM→ T<sup>*</sup> M is the musical isomorphism [6] defined by g) and the pseudo-Riemannian tensor g of M respectively.

DOI Code: 10.1285/i15900932v8n1p123

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