On statistical almost contact manifolds

This paper investigates the interplay between statistical geometry, Lie group theory, and almost contact metric structures. We focus on left-invariant statistical almost contact structures on Lie groups, particularly those of type II, where the Lie bracket remains within the span of the bracketed elements. Key results include the characterization of Lie groups with a 1-dimensional center, the properties of their associated equiaffine connections, and the behavior of statistical curvature tensors. We also establish conditions for conjugate symmetric structures and explore statistical structures derived from the Hessians of smooth functions. These findings reveal new connections between statistical geometry, Lie groups, and potential theory. All results are supported by illustrative examples that provide deeper insights into their implications.