Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 1, pp. 103-114 (2008)

Dual connections in Finsler geometry

T. Nagano and T. Aikou

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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