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On osculation of homogeneous connections. (English) Zbl 0794.53016
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 457-468 (1992).
Osculation of “nonlinear objects” by “linear” ones is an important tool of Finsler geometry applied mainly by A. Moór using classical tensor calculus. The author presents a general and modern formulation of this idea in the language of fiber bundles. Starting from a homogeneous (nonlinear) connection $$H$$ in a vector bundle and osculating a (deflection free) Finsler pair connection $$(H^ B,H)$$ along a section $$\sigma$$, he constructs a linear connection $$H^ \sigma$$ in the vector bundle whose geodesics have second order contact with the geodesics of $$H$$. An illuminating description of the Berwald connection and some applications complete the paper.
For the entire collection see [Zbl 0764.00002].
##### MSC:
 53C05 Connections (general theory) 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)