The Gauge Equation in Statistical Manifolds: An Approach through Spectral Sequences

Michel Nguiffo Boyom and Stephane Puechmorel ()
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Michel Nguiffo Boyom: IMAG CNRS, University of Montpellier, 499-554 Rue du Tuel, 34090 Montpellier, France
Stephane Puechmorel: Laboratoire ENAC, University of Toulouse, 7 Avenue Edouard Belin, 31055 Toulouse, France

Mathematics, 2024, vol. 12, issue 8, 1-19

Abstract: The gauge equation is a generalization of the conjugacy relation for the Koszul connection to bundle morphisms that are not isomorphisms. The existence of nontrivial solution to this equation, especially when duality is imposed upon related connections, provides important information about the geometry of the manifolds under consideration. In this article, we use the gauge equation to introduce spectral sequences that are further specialized to Hessian structures.

Keywords: gauge equation; spectral sequence; KV-cohomology; Hessian manifold; statistical manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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