Investigating Statistical Submersions and Their Properties

Abstract

This research aims to prove a sharp relationship between statistical submersions and doubly minimal immersions. We consider a non-trivial statistical submersion on a statistical manifold with isometric fibers. Then, we investigate that it cannot be isometrically immersed as a doubly minimal manifold into any statistical manifold of non-positive sectional curvature using a submersion invariant for dual connections and additional conditions.

Keywords

• statistical manifolds
• statistical submersions
• doubly minimal immersions
• scalar curvature
• isometric fibers
• submersion invariants