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

Author

Listed:
  • Michel Nguiffo Boyom

    (IMAG CNRS, University of Montpellier, 499-554 Rue du Tuel, 34090 Montpellier, France
    These authors contributed equally to this work.)

  • Stephane Puechmorel

    (Laboratoire ENAC, University of Toulouse, 7 Avenue Edouard Belin, 31055 Toulouse, France
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Michel Nguiffo Boyom & Stephane Puechmorel, 2024. "The Gauge Equation in Statistical Manifolds: An Approach through Spectral Sequences," Mathematics, MDPI, vol. 12(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1177-:d:1375538
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