Liftings of 1-forms to the bundle of affinors (Q2769243)

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.