Basic cohomology group decomposition of K-contact 5-manifolds

الأصل · EN

In this paper, we consider decompositions of basic degree 2 cohomology for a compact K-contact 5-manifold (M,ξ,η,Φ,g), and conclude the pureness and fullness of Φ-invariant and Φ-anti-invariant cohomology groups. Moreover, we discuss the decomposition of the complexified basic degree 2 cohomology group. This is an analogue problem when Draghici, Li and Zhang DLZ1 considered the C∞ pureness and fullness of J-invariant and J-anti-invariant subgroups of the degree 2 real cohomology group H²(M,R) of any compact almost complex manifold (M, J).