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\iteman{io-port 05037143}
\itemau{Sato, Takuji}
\itemti{On a family of almost K\"ahler structures on the tangent bundles over some statistical models.}
\itemso{Matsushita, Yasuo (ed.) et al., Topics in almost Hermitian geometry and related fields. Proceedings in honor of Prof. K. Sekigawa's 60th birthday, Niigata, Japan, November 1--3, 2004. Hackensack, NJ: World Scientific (ISBN 981-256-417-9/hbk). 215-225 (2005).}
\itemab
It is well known that a Riemannian metric on a manifold $M$ induces an almost K\"ahler structure on the tangent bundle $TM$. More generally an analogous construction can be carried out for a torsion free affine connection on a Riemannian manifold $(M,g)$ whose dual connection with respect to $g$ is torsion free, too. Here the author applies this idea to statistical models endowed with the Fisher information as Riemannian metric and the so-called family of $\alpha$-connections. This is carried out explicitly for the manifolds of normal distributions and of discrete distributions on a finite set. It is shown that for special values of $\alpha$ one actually obtains a K\"ahler structure with constant holomorphic sectional curvature.
\itemrv{Andreas Cap (Wien)}
\itemcc{}
\itemut{almost K\"ahler structure; tangent bundle; statistical model; Fisher information}
\itemli{}
\end