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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
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