https://hal-enac.archives-ouvertes.fr/hal-02910182Puechmorel, StéphaneStéphanePuechmorelENAC - Ecole Nationale de l'Aviation CivileLifting Dual Connections with the Riemann ExtensionRelévement de connexions duales sur le fibré cotangentHAL CCSD2020information geometrydual connectionsRiemannian extensioncotangent bundle[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]puechmorel, stephane2020-07-31 21:51:222021-11-03 04:17:592020-08-03 15:28:03enJournal articleshttps://hal-enac.archives-ouvertes.fr/hal-02910182/document10.3390/math8112079application/pdf1Le (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.