Investigating Statistical Submersions and Their Properties

Aliya Naaz Siddiqui and Fatimah Alghamdi ()
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Aliya Naaz Siddiqui: Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, India
Fatimah Alghamdi: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 17, 1-14

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; dual affine connections (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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