All natural concomitants of vector valued differential forms. (English) Zbl 0642.53017

Kolář, Ivan; Michor, Peter W.

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

Keywords:

differential forms; natural concomitant; Fröhlicher-Nijenhuis bracket; inner products; wedge product; exterior derivations; contractions

Citations:

Zbl 0634.00015