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

Jonatan Lenells, Gerard Misiolek

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…