Dual connections in Finsler geometry

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

T. Aikou¹  T. Nagano¹ 

[1] Siebold University of Nagasaki, Kagoshima University

关键词: dual connections;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

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.

【 授权许可】

Unknown