Mathematics (Apr 2024)

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

  • Michel Nguiffo Boyom,
  • Stephane Puechmorel

DOI
https://doi.org/10.3390/math12081177
Journal volume & issue
Vol. 12, no. 8
p. 1177

Abstract

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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.

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