Lifting Dual Connections with the Riemann Extension

Stéphane Puechmorel
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Stéphane Puechmorel: ENAC, Université de Toulouse, 31000 Toulouse, France

Mathematics, 2020, vol. 8, issue 11, 1-15

Abstract: Let ( 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 are 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 obtained, allowing the definition of dual connections on T T * M with respect to the Riemannian extension. This work was motivated by the general problem of finding the projective limit of a sequence of a finite-dimensional statistical manifold.

Keywords: information geometry; dual connections; Riemannian extension; cotangent bundle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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