## On naturality of the Helmholtz operator.(English)Zbl 1112.58004

The Helmholtz map in the $$r$$-th order variational calculus on a fibered manifold $$Y\to M$$ can be interpreted as a differential operator transforming base preserving morphisms from $$J^{2r} Y$$ into $$V^*Y\otimes \bigwedge ^m T^*M$$ into base preserving morphisms from $$J^{4r} Y$$ into $$V^* J^{2r} Y \otimes V^* Y\otimes \bigwedge ^m T^*M$$, $$m= \dim M$$.
The author deduces that all natural operators of this type are the constant multiples of the Helmholtz operator.

### MSC:

 58A20 Jets in global analysis

### Keywords:

natural operator; Euler morphism
Full Text: