%0 Conference Paper %F Oral %T Canonical Foliations of Statistical Manifolds with Hyperbolic Compact Leaves %+ Ecole Nationale de l'Aviation Civile (ENAC) %+ Institut Montpelliérain Alexander Grothendieck (IMAG) %A Gnandi1, Emmanuel %A Boyom, Michel %A Puechmorel, Stéphane %< avec comité de lecture %B 5th International Conference on Geometric Science of Information (GSI) %C Paris, France %P 371–379 %8 2021-07-21 %D 2021 %R 10.1007/978-3-030-80209-7_41 %K Mathematic %K Computer science %Z Mathematics [math]/Differential Geometry [math.DG] %Z Computer Science [cs]Conference papers %X A. 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. %G English %2 https://enac.hal.science/hal-03609559/document %2 https://enac.hal.science/hal-03609559/file/gsi2021%20%281%29.pdf %L hal-03609559 %U https://enac.hal.science/hal-03609559 %~ ENAC %~ CNRS %~ I3M_UMR5149 %~ INSMI %~ IMAG-MONTPELLIER %~ MIPS %~ UNIV-MONTPELLIER %~ UM-2015-2021