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Lifting Dual Connections with the Riemann Extension
Lifting Dual Connections with the Riemann Extension
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.
Littérature citée [13 références]
https://hal-enac.archives-ouvertes.fr/hal-02910182
Contributeur : stephane puechmorel Connectez-vous pour contacter le contributeur
Soumis le : vendredi 31 juillet 2020 - 21:51:22
Dernière modification le : mercredi 3 novembre 2021 - 04:17:59
Contributeur : stephane puechmorel Connectez-vous pour contacter le contributeur
Soumis le : vendredi 31 juillet 2020 - 21:51:22
Dernière modification le : mercredi 3 novembre 2021 - 04:17:59
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lift_dual_connections.pdf
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