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arXiv · 1710.00681

Amari Functors and Dynamics in Gauge Structures

Michel Nguiffo Boyom·Ahmed Zeglaoui
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Abstract

We deal with finite dimensional differentiable manifolds. All items are concerned with are differentiable as well. The class of differentiability is $C^\infty$. A metric structure in a vector bundle $E$ is a constant rank symmetric bilinear vector bundle homomorphism of $E\times E$ in the trivial bundle line bundle. We address the question whether a given gauge structure in $E$ is metric. That is the main concerns. We use generalized Amari functors of the information geometry for introducing two index functions defined in the moduli space of gauge structures in $E$. Beside we introduce a differential equation whose analysis allows to link the new index functions just mentioned with the main concerns. We sketch applications in the differential geometry theory of statistics. Reader interested in a former forum on the question whether a giving connection is metric are referred to appendix.

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Michel Nguiffo Boyom, Ahmed Zeglaoui. 2017-09-27. Amari Functors and Dynamics in Gauge Structures. https://doi.org/10.1007/978-3-319-68445-1_20

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