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Lifting dual connections to the cotangent bundle

Abstract : 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.
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Contributor : Stephane Puechmorel <>
Submitted on : Friday, July 31, 2020 - 9:51:22 PM
Last modification on : Monday, August 17, 2020 - 10:12:15 AM


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  • HAL Id : hal-02910182, version 1



Stéphane Puechmorel. Lifting dual connections to the cotangent bundle. In press. ⟨hal-02910182⟩



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