2015/11/24 by Paolo Perrone, Perrone, Paolo
Physics and Astronomy · #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1511.07737
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.