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Zbl 0642.53034
Kis, Bela
Connection theory and parameter transformations. (English)
[A] Geometry and physics, Proc. Winter Sch., Srní/Czech. 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 16, 85-99 (1987).

[For the entire collection see Zbl 0634.00015.] \par The classical connection theory on fiber bundles has two types of symmetries: the fiber symmetry, related to the fiber group of the fiber bundle and a hidden symmetry, related to the notion of parameter transformations of smooth curves. In this last case, if we consider the parallel translation as an operator mapping the curves of the base manifold to curves of the total space, then this operator commutes with the parameter transformation of curves. In this paper the author proposes to give a description of a connection theory in which the above commutation condition is geometrically clarified. An application from Finsler geometry, using Rund's $\delta$-derivation, is sketched at the end.
[P.R.Rodrigues]

MSC 2000:: *53C05 Connections, general theory
53C60 Finsler spaces and generalizations (global)

Keywords: parameter transformations; connection; fiber bundles; commutation condition; Finsler geometry

Citations: Zbl 0634.00015

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