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On Finsler connections. (English) Zbl 0804.53030
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, 649-661 (1992).
From the preface: “We shall discuss new basic ideas concerning Finsler connections. Our approach uses two key notions: horizontal structure and (general) pseudo-connection. We hope that this new approach will result in a real conceptual and technical simplification of M. Matsumoto’s well-known theory [Foundations of Finsler geometry and special Finsler spaces (Kaiseisha Press, 1986; Zbl 0594.53001)]. Also, it may be helpful in better understanding the “pure essence” of Finsler connections. Our ideas also have natural relations with the recent theory of R. Miron and M. Anastasiei [Vector bundles, Lagrange spaces and applications in relativity theory, Bucureşti (1987; Zbl 0616.53002)]. Miron’s theory is more general than ours in the sense that it works on the whole tangent bundle of the total space of a vector bundle, while we limit ourselves to the vertical subbundle. However, this restriction is perfectly adequate with the demands of classical Finsler geometry”.
For the entire collection see [Zbl 0764.00002].
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)