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arXiv · 1210.5476

Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups

Jonatan Lenells·Gerard Misiolek
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Abstract

We study the family of $α$-connections of Amari-Chentsov on the homogeneous space $\mathcal{D}(M)/\mathcal{D}_μ(M)$ of diffeomorphisms modulo volume-preserving diffeomorphims of a compact manifold $M$. We show that in some cases their geodesic equations yield completely integrable Hamiltonian systems.

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Jonatan Lenells, Gerard Misiolek. 2012-10-19. Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups. https://arxiv.org/abs/1210.5476

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