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05037143 Sato, Takuji On a family of almost K\"ahler structures on the tangent bundles over some statistical models. 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). 2005 Hackensack, NJ: World Scientific EN almost K\"ahler structure tangent bundle statistical model Fisher information 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. Andreas Cap (Wien)