Statistical Warped Product Immersions into Statistical Manifolds of (Quasi-)Constant Curvature

Abstract

Warped products provide an elegant and versatile framework for exploring and understanding a wide range of geometric structures. Their ability to combine two distinct manifolds through a warping function introduces a rich and diverse set of geometries, thus making them a powerful tool in various mathematical, physical, and computational applications. This article addresses the central query related to warped product submanifolds in the context of statistics. It focuses on deriving two new and distinct inequalities for a statistical warped product submanifold in a statistical manifold of a constant (quasi-constant) curvature. This article then finishes with some concluding remarks.

Keywords

• statistical warped products
• statistical manifolds
• Laplacian operators
• statistical immersions
• quasi-constant curvature
• dual connections