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.
![d<sup>ω</sup>=d+e(ω) (e(ω)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/00e10197f3cbb2e504a1c34cdb3e56b2.png)
![ω](http://siba-ese.unile.it/plugins/generic/latexRender/cache/45bf03a575f6e81359314e906fb2bff3.png)
![u∈ M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/9edcf226226da519e3133bb7a56662e8.png)
![d<sup>ω</sup> u=0](http://siba-ese.unile.it/plugins/generic/latexRender/cache/3f39f82a4afd53d4229ab8d526d46585.png)
![d<sup>ω</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/219d5b3b77f922c1c193b0e26199e509.png)
![(m + 2,m)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/faf2faf13745e379b9d2df1a66df9b30.png)
![M(U, ω, \xi_𝛼, η^𝛼,g)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/b1e4a9659585b0067486a63f6872e039.png)
![(U,ω,\xi_𝛼,η^𝛼,g)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/9b6662d9d16eca05aa5456481d4c413b.png)
![2m](http://siba-ese.unile.it/plugins/generic/latexRender/cache/93b47baf59ea142b485dc22577a56dac.png)
![\xi_𝛼; 𝛼=2m+1, 2m+2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4f7332dd7ad36d6ce1385d158fc909ea.png)
![η^𝛼=\flat(\xi_𝛼)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/08f0ba6df00f01fe564201f7272acf11.png)
![\flat: TM→ T<sup>*</sup> M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4e3e94c5da13ef34ad94c29f2935b619.png)
DOI Code:
10.1285/i15900932v8n1p123
Full Text: PDF