Geometry of tangent and cotangent bundles on statistical manifolds

Tat Dat Tô (1, 2) , Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 IMT - Institut de Mathématiques de Toulouse UMR5219

This note surveys some results on the geometric structure on the tangent bundle and cotangent bundle of statistical manifolds. We also study the completeness of the tangent bundle with respect to the Sasaki metrics induced from the statistical structures.

Domaines: Géométrie différentielle [math.DG]; Probabilités [math.PR]; Variables complexes [math.CV]

Tat Dat Tô, Stéphane Puechmorel. Geometry of tangent and cotangent bundles on statistical manifolds. 2019. ⟨hal-02056897v2⟩