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On certain geometrical structures on the bundle of jets of differentiable mappings. (English. Russian original) Zbl 0853.58008
Russ. Math. 39, No. 7, 48-61 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 7, 51-64 (1995).
Within the bundle of 1-jets of differentiable mappings, the author describes the lifts of functions, 1-forms and vector fields, the tensor product of lifts, the horizontal lifts of vector fields and 1-forms – with respect to a given linear connection, the prolongation of Riemannian metrics, and the horizontal and synectic lifts of linear connections.
Finally, a characterization for the infinitesimal projective transformation of the synectic lift of a torsion-free linear connection is provided.
58A20 Jets in global analysis
58C25 Differentiable maps on manifolds
53B05 Linear and affine connections