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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.
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Contributor : Stephane Puechmorel Connect in order to contact the contributor
Submitted on : Friday, July 31, 2020 - 9:51:22 PM
Last modification on : Wednesday, November 3, 2021 - 4:17:59 AM


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Stéphane Puechmorel. Lifting Dual Connections with the Riemann Extension. Mathematics , MDPI, 2020, Special Issue Geometry and Topology in Statistics, 8 (11), pp.2079. ⟨10.3390/math8112079⟩. ⟨hal-02910182⟩



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