Dual Connections and Holonomy

Paolo Perrone

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arXiv · 1511.07737

Dual Connections and Holonomy

Paolo Perrone

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Abstract

Dual affine connections on Riemannian manifolds have played a central role in the field of information geometry since their introduction by Amari. Here I would like to extend the notion of dual connections to general vector bundles with an inner product, in the same way as a unitary connection generalizes a metric affine connection, using Cartan decompositions of Lie algebras. This gives a natural geometric interpretation for the Amari tensor, as a "connection form term" which generates dilations, and which is reversed for the dual connections.

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Paolo Perrone. 2015-11-24. Dual Connections and Holonomy. https://arxiv.org/abs/1511.07737

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