On Contact CR-Product of Sasakian statistical manifold

TL;DR

This paper explores the geometric properties of contact CR-submanifolds within Sasakian statistical manifolds, focusing on integrability, geodesic conditions, and introducing a statistical contact CR-product concept.

Contribution

It introduces the statistical contact CR-product and characterizes integrability and geodesic conditions for submanifolds in Sasakian statistical manifolds.

Findings

Characterization of integrability of invariant and anti-invariant distributions

Results on D-totally geodesic and D-umbilic contact CR submanifolds

Introduction of the statistical contact CR-product concept

Abstract

This paper studies the geometric properties of contact CR-submanifolds of Sasakian statistical manifold. The integrability of invariant and anti-invariant distributions of contact CR-submanifolds has been characterized. Results on D-totally geodesic, mixed totally geodesic and D-umbilic contact CR submanifolds with regard to dual connections in statistical manifolds have been developed. The statistical version of contact CR-product of Sasakian statistical manifold has been introduced.