https://enac.hal.science/hal-03609559Gnandi1, EmmanuelEmmanuelGnandi1ENAC - Ecole Nationale de l'Aviation CivileBoyom, MichelMichelBoyomIMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche ScientifiquePuechmorel, StéphaneStéphanePuechmorelENAC - Ecole Nationale de l'Aviation CivileCanonical Foliations of Statistical Manifolds with Hyperbolic Compact LeavesHAL CCSD2021MathematicComputer science[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG][INFO] Computer Science [cs]puechmorel, stephane2022-03-15 16:15:212023-07-15 04:10:172022-03-22 16:31:14enConference papershttps://enac.hal.science/hal-03609559/document10.1007/978-3-030-80209-7_41application/pdf1A. The sheaf of solutions (J ,∇) of the Hessian equation on a gauge structure (M, ∇) is a key ingredient for understanding important properties from the cohomological point of view. In this work, a canonical representation of the group associated by Lie third's theorem to the Lie algebra formed by the sections of (J, ∇) is introduced. On the foliation it defines, a characterization of compact hyperbolic leaves is then obtained. We conclude that these leaves are equipped with a statistical model structure.