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All natural concomitants of vector valued differential forms. (English) Zbl 0642.53017
Geometry and physics, Proc. Winter Sch., Srní/Czech. 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 16, 101-108 (1987).
[For the entire collection see Zbl 0634.00015.]
Let M be a \(C^{\infty}\)-manifold, TM its tangent bundle, \(\Omega^ p\) the space of TM-valued differential forms of order p on M. A natural concomitant in this context is understood to be a bilinear map \(\Omega^ p\times \Omega^ q\to \Omega^{p+q}\) commuting with pullbacks of local diffeomorphism of manifolds. It is proved, that for dim \(M\geq p+q+1\) the natural concomitants form a vector space generated by 10 natural operations under which is the Fröhlicher-Nijenhuis bracket, the others being constructed by inner products, wedge product, exterior derivations and contractions.
Reviewer: K.Horneffer

MSC:
53A55 Differential invariants (local theory), geometric objects
58A10 Differential forms in global analysis