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

Jonatan Lenells; Gerard Misiolek

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

Differential Geometry 2012-10-22 v1 Exactly Solvable and Integrable Systems

Authors: Jonatan Lenells , Gerard Misiolek

Abstract

We study the family of $\alpha$ -connections of Amari-Chentsov on the homogeneous space $\mathcal{D}(M)/\mathcal{D}_\mu(M)$ 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.

Keywords

Amari-Chentsov connections homogeneous spaces diffeomorphism groups geodesic equations integrable Hamiltonian systems volume-preserving diffeomorphisms

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@article{arxiv.1210.5476,
  title  = {Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups},
  author = {Jonatan Lenells and Gerard Misiolek},
  journal= {arXiv preprint arXiv:1210.5476},
  year   = {2012}
}

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11 pages

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

Abstract

Keywords

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