On CR-statistical submanifolds of holomorphic statistical manifolds

TL;DR

This paper explores properties of CR-statistical submanifolds within holomorphic statistical manifolds, providing characterizations, curvature relations, and examples to deepen understanding of their geometric structure.

Contribution

It introduces new characterizations of CR-products and establishes a relationship between Ricci curvature and mean curvature in these submanifolds.

Findings

Characterization of CR-products in holomorphic statistical manifolds

Relationship between Ricci curvature and squared mean curvature

Examples illustrating theoretical results

Abstract

In the present paper, we investigate some properties of the distributions involved in the definition of a CR-statistical submanifold. The characterization of a CR-product in holomorphic statistical manifolds is given. By using an optimization technique, we establish a relationship between the Ricci curvature and the squared norm of the mean curvature of any submanifold in the same ambient space. The equality case is also discussed here. This paper finishes with some related examples.