# zbMATH — the first resource for mathematics

Liftings of 1-forms to the bundle of affinors. (English) Zbl 1020.58005
The following theorem is proved: The space of natural operators $$T^*\rightsquigarrow T^*(T\otimes T^*)$$ over $$n$$-dimensional manifolds form a free $$n$$-dimensional module over the algebra of functions $$C^\infty$$. An explicit basis is found. Non-existence of canonical volume (and hence symplectic, contact, oriented Riemannian etc.) forms on certain tensorial bundles is deduced.
##### MSC:
 58A20 Jets in global analysis 53A55 Differential invariants (local theory), geometric objects
##### Keywords:
natural bundles; natural operators