Lifting Dual Connections with the Riemann Extension

Relévement de connexions duales sur le fibré cotangent

Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

Le (M, g) be a Riemannian manifold equipped with a pair of dual connections (∇, ∇ *).Such a structure is known as a statistical manifold since it was defined in the context of information geometry. This paper aims at defining the complete lift of such a structure to the cotangent bundle T * M using the Riemannian extension of the Levi-Civita connection of M.In the first section, common tensors associated with pairs of dual connections, emphasizing the cyclic symmetry property of the so-called skewness tensor. In a second section, the complete lift of this tensor is 6 obtained, allowing the definition of dual connections on TT * M with respect to the Riemannian extension.

Mots clés: information geometry; dual connections; Riemannian extension; cotangent bundle

Domaines: Géométrie différentielle [math.DG]

Stéphane Puechmorel. Lifting Dual Connections with the Riemann Extension. Mathematics , In press, Special Issue Geometry and Topology in Statistics, 8 (11), pp.2079. ⟨10.3390/math8112079⟩. ⟨hal-02910182⟩