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- W151577916 abstract "In this paper we give a new definition of the classical contact elements of a smooth manifold M as ideals of its ring of smooth functions: they are the kernels of Weil's near points. Ehresmann's jets of cross-sections of a fibre bundle are obtained as a particular case. The tangent space at a point of a manifold of contact elements of M is shown to be a quotient of a space of derivations from the same ring C ∞(M) into certain finite-dimensional local algebras. The prolongation of an ideal of functions from a Weil bundle to another one is the same ideal, when its functions take values into certain Weil algebras; following the same idea vector fields are prolonged, without any considerations about local one-parameter groups. As a consequence, we give an algebraic definition of Kuranishi's fundamental identification on Weil bundles, and study their affine structures, as a generalization of the classical results on spaces of jets of cross-sections." @default.
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- W151577916 date "2000-12-01" @default.
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- W151577916 title "Weil bundles and jet spaces" @default.
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- W151577916 doi "https://doi.org/10.1023/a:1022408527395" @default.
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