Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 26, No. 2, pp. 349-358 (2010)

On the parallel displacement and parallel vector fields in Finsler Geometry

Tetsuya Nagano

University of Nagasaki

Abstract: In Finsler geometry, the notion of parallel for Finsler tensor fields is defined, already. In this paper, however, for vector fields on a base manifold, the author studies the notion of parallel. In the last section, the obtained results are shown as compare corresponding properties to them of Riemannian geometry.

Keywords: Finsler geometry, vector field, parallel displacement, path, autoparallel, geodesic

Classification (MSC2000): 53B40

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