Curvature bounded conjugate symmetric statistical structures with complete metric

TL;DR

This paper generalizes key theorems on complete affine spheres to statistical structures on manifolds, replacing constant curvature assumptions with curvature inequalities, broadening the scope of geometric analysis.

Contribution

It introduces generalized theorems for statistical structures with curvature inequalities, extending classical results beyond constant curvature cases.

Findings

Generalized theorems for affine spheres on statistical manifolds

Curvature inequalities replace constant curvature assumptions

Broadened applicability of geometric structures in statistical contexts

Abstract

In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the curvature satisfies some inequalities.