The natural operators $T^{(0,0)} ⇝ T^{(1,1)}T^{(r)}$

Włodzimierz M. Mikulski

The natural operators

T^{(0, 0)} ⇝ T^{(1, 1)} T^{(r)}

Włodzimierz M. Mikulski

Colloquium Mathematicae, Tome 96 (2003), p. 5-16 / Harvested from The Polish Digital Mathematics Library

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Résumé

We study the problem of how a map f:M → ℝ on an n-manifold M induces canonically an affinor $A (f) : T T^{(r)} M \to T T^{(r)} M$ on the vector r-tangent bundle $T^{(r)} M = (J^{r} (M, ℝ) ₀) *$ over M. This problem is reflected in the concept of natural operators $A : T_{| ℳ f ₙ}^{(0, 0)} ⇝ T^{(1, 1)} T^{(r)}$ . For integers r ≥ 1 and n ≥ 2 we prove that the space of all such operators is a free (r+1)²-dimensional module over $^{\infty} (T^{(r)} ℝ)$ and we construct explicitly a basis of this module.

Publié le : 2003-01-01

Zbl 1036.58006

EUDML-ID : urn:eudml:doc:285093

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     author = {W\l odzimierz M. Mikulski},
     title = {The natural operators $T^{(0,0)} \textasciitilde\ T^{(1,1)}T^{(r)}$
            },
     journal = {Colloquium Mathematicae},
     volume = {96},
     year = {2003},
     pages = {5-16},
     zbl = {1036.58006},
     language = {en},
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Włodzimierz M. Mikulski. The natural operators $T^{(0,0)} ⇝ T^{(1,1)}T^{(r)}$
            . Colloquium Mathematicae, Tome 96 (2003) pp. 5-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-2/