Statistical Warped Products and Their Generalizations in Holomorphic Statistical Manifolds

In the field of differential geometry and mathematical physics, warped products consistently hold a central position. This paper focuses on the advancement of statistical warped products, where we examine the generic submanifolds in a holomorphic statistical manifold. We expand this exploration to study warped product CR-statistical submanifolds, presenting general inequalities in the statistical context. Subsequently, we make use of the concept of warped product CR-statistical submanifolds to introduce the notion of a twisted product CR-statistical submanifold, along with its extension, the doubly twisted product CR-statistical submanifold. Moreover, we demonstrate that a twisted product CR-statistical submanifold inherently qualifies as a CR-product. Additionally, we conclusively prove that no doubly twisted product CR-statistical submanifolds exist except twisted product CR-statistical submanifolds.