Basic Cohomology Group Decomposition of K-Contact 5-Manifolds

Abstract

In this paper, we consider decompositions of basic degree 2 cohomology for a compact K-contact 5-manifold \({(M,\xi,\eta,\Phi,g)}\), and conclude the pureness and fullness of \({\Phi}\)-invariant and \({\Phi}\)-anti-invariant cohomology groups. Moreover, we discuss the decomposition of the complexified basic degree 2 cohomology group. This is an analogue problem when Draghici et al. (Int Math Res Not IMRN 2010(1):1–17, 2010) considered the \({C^{\infty}}\) pureness and fullness of J-invariant and J-anti-invariant subgroups of the degree 2 real cohomology group \({H^2(M,{\mathbb{R}})}\) of any compact almost complex manifold (M, J).