1976
DOI: 10.4310/jdg/1214433720
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Prolongation of connections to bundles of infinitely near points

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1983
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Cited by 55 publications
(44 citation statements)
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“…A lifting (the so-called complete lifting) of connections to Weil bundles was constructed long ago in [5]. But the problem of finding all such liftings is still unsolved and seems to be hard.…”
mentioning
confidence: 99%
See 1 more Smart Citation
“…A lifting (the so-called complete lifting) of connections to Weil bundles was constructed long ago in [5]. But the problem of finding all such liftings is still unsolved and seems to be hard.…”
mentioning
confidence: 99%
“…This paper contains a classification of all affine liftings of torsion-free linear connections on n-dimensional manifolds to any linear connections on Weil bundles under the condition that n ≥ 3.A lifting (the so-called complete lifting) of connections to Weil bundles was constructed long ago in [5]. But the problem of finding all such liftings is still unsolved and seems to be hard.…”
mentioning
confidence: 99%
“…Some of them were applied in constructions on connections (see e.g. [3], [7]). In Section 8, using the flow operator W r we construct a principal connection W r (Γ, Λ) on the principal bundle W r P → P .…”
mentioning
confidence: 99%
“…To obtain such constructions, some vector fields obtained from right-invariant vector fields are useful (see e.g. [7] in the case of the trivial Lie group G = {e}). Taking into account the above remarks, we see that a complete classification of all PB m (G)-gauge-natural operators A : T G-inv T W r in the sense of Definition 1 is especially important.…”
mentioning
confidence: 99%
“…for every n-dimensional manifold M and every linear connection ∇ on M , where ∇ A denotes the complete lift of ∇ (see [14], [7]), T and R the torsion and curvature tensors of ∇ and G ′ H ′′…”
mentioning
confidence: 99%