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The structure tensor and first order natural differential operators. (English) Zbl 0785.53014

In analogy to the structure tensor of a \(G\)-structure, the author introduces the notion of a structure tensor for sections of a first order natural bundle \(F\) with homogeneous standard fibre and presents several concrete examples. Then he proves that every first order natural operator of \(F\) into another first order natural bundle \(E\) factorizes through a natural transformation of the bundle of structure tensors of \(F\) into \(E\). As an application of the latter result, all first order natural operators transforming pairs of vector fields into vector fields are determined.
Reviewer: I.Kolář (Brno)

MSC:

53A55 Differential invariants (local theory), geometric objects
53C10 \(G\)-structures
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