In this paper, we first investigate the Kenmotsu statistical structures built on a space form and determine some special under two curvature conditions. Secondly, show that if holomorphic sectional of hypersurface orthogonal to structure vector in manifold is constant, then $\phi-$sectional ambient must be constant $-1$, $0$. addition, non-trivial examples are given illustrate results paper.

In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was an analytic expression for third structure or f -holomorphic sectional GK -manifold. We separated classes manifolds and collected their local characterization.