Almost contact Kähler manifolds of constant holomorphic sectional curvature

Abstract

We introduce the notion of an almost contact K¨ahler structure. We also define the holomorphic sectional curvature of the distribution of an almost contact K¨ahler structure with respect to an interior metric connection and establish relations between the ϕ-sectional curvature of an almost contact K¨ahler manifold and the holomorphic sectional curvature of the distribution of an almost contact K¨ahler structure.

Almost contact metric structures defined by an $N$-prolonged connection

“…and it is called the Reeb vector field. In this subsection we will pay more attention to the so called almost contact Kählerian spaces [5], other basic classes of of almost contact metric spaces will be considered in the next section.…”