Euler and Chen-invariant type inequalities on submanifolds in Golden statistical manifolds

Abstract

The purpose of this research paper is to analyze the statistical manifolds coupled with Golden structure. On golden-like statistical manifolds, we derive several basic attributes for the intrinsic and extrinsic invariants of statistical submanifolds in golden-like statistical manifolds. Also, we derive an Euler inequality for submanifolds in golden-like statistical manifolds.  Moreover, we used particular types of second fundamental forms of Chen-invariant type inequalities for these classes of submanifolds in golden-like statistical manifolds to characterize the equality case. We strengthen our idea with an example as well.