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Kureš, Miroslav; Mikulski, Włodzimierz M.

Natural operators lifting vector fields to bundles of Weil contact elements. (English) Zbl 1080.58005

Czech. Math. J. 54, No. 4, 855-867 (2004).
Summary: Let \(A\) be a Weil algebra. The bijection between all natural operators lifting vector fields from \(m\)-manifolds to the bundle functor \(K^A\) of Weil contact elements and the subalgebra of fixed elements \(SA\) of the Weil algebra \(A\) is determined and the bijection between all natural affinors on \(K^A\) and \(SA\) is deduced. Furthermore, the rigidity of the functor \(K^A\) is proved. Requisite results about the structure of \(SA\) are obtained by a purely algebraic approach, namely the existence of nontrivial \(SA\) is discussed.

Cited in 2 Documents

MSC:

58A32 Natural bundles
12D05 Polynomials in real and complex fields: factorization
58A20 Jets in global analysis
53A55 Differential invariants (local theory), geometric objects

Keywords:

Weil algebra; Weil bundle; contact element; natural operator
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References:

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