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Włodzimierz M. Mikulski (2006)
Archivum Mathematicum
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We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.
Ivan Kolár (1996)
Extracta Mathematicae
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We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.
Jan Kurek, Włodzimierz Mikulski (2008)
Annales UMCS, Mathematica
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All natural operators T ↝ T(T ⊗ T*) lifting vector fields X from n-dimensional manifolds M to vector fields B(X) on the bundle of affinors ™ ⊗ T*M are described.
Kolář, Ivan
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The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of . It is deduced that under certain assumptions on , all natural operators of the second type can be constructed through those of the first one.