Siebold University of Nagasaki, Kagoshima University
Abstract: In the present paper, we generalize the notion of statistical structure and its dual connection in Riemannian geometry to Finsler geometry. We shall show that the Berwald connection D of a Finsler manifold is a statistical structure. In particular, as an application of this fact, we shall show that, if the hh-curvature of the Berwald connection D vanishes identically, then the given Finsler metric induces a Hessian metric on the base manifold.
Keywords: Finsler connections, dual connections
Classification (MSC2000): 53B40
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