Commuting statistical Jacobi operators

Abstract

This paper extends the classical theory of Jacobi operators to statistical manifolds, integrating concepts from differential and information geometry. We analyze the commutation properties of statistical Jacobi operators and establish their implications for the geometry of statistical hypersurfaces. By generalizing results on commuting curvature operators, we derive new insights into the structure of statistical manifolds. Our findings contribute to a deeper understanding of the interplay between curvature, shape operators, and statistical connections.