ϕ-sectional curvature of statistical structures on almost contact metric manifolds

Abstract

We introduce the notion of ϕ -sectional K -curvature on almost contact statistical manifolds by combining the sectional K -curvature of a statistical structure with the classical ϕ -sectional curvature in almost contact geometry. We prove that this curvature is always non-positive and show that it vanishes precisely when the difference tensor satisfies for every vector field orthogonal to the Reeb vector field. Several equivalent characterizations of the vanishing case are obtained in terms of algebraic and curvature conditions. In addition, we study statistical connections that are compatible with the structure tensor ϕ and prove that any almost contact statistical manifold admitting a ϕ -compatible statistical connection must be a cosymplectic statistical manifold with zero ϕ -sectional K -curvature. Explicit examples are presented to illustrate the results.