%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