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A Finsler metric of a manifold or vector bundle is defined as a smooth assignment for each base point a norm on each fibre space, and thus the class of Finsler metrics contains Riemannian metrics as a special sub-class. For this reason, Finsler geometry is usually treated as a generalization of Riemannian geometry. In fact, there are many contributions to… (More)
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… (More)
In the present paper, we shall prove new characterizations of Berwald spaces and Landsberg spaces. The main idea inthis research is the use of the so-called average Riemannian metric.