Hyperbolicity of the Compact Leaves of Statistical Manifold Foliations

Michel Boyom (1) , Emmanuel Gnandi (2) , Stéphane Puechmorel (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 ENAC - Ecole Nationale de l'Aviation Civile

In this work, we show a construction of a Hessian foliation on a statistical manifold. Our results provide conditions, under which the compacts hessian leaves (up to diffeomorphism) are quotients of homogeneous convex cones.

Domaines: Mathématiques [math]

Michel Boyom, Emmanuel Gnandi, Stéphane Puechmorel. Hyperbolicity of the Compact Leaves of Statistical Manifold Foliations. 2021. ⟨hal-03008361v2⟩