Some results on Kenmotsu statistical manifolds

Abstract

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