The natural operators lifting 1 - forms to the r - jet prolongation of the cotangent bundle 1
نویسندگان
چکیده
First, we classify all natural operators T |M fn T (0,0)(Jr T ∗) transforming vector fields to functions on the r -jet prolongation Jr T ∗ of the cotangent bundle. Next, we classify natural operators T ∗|M fn T ∗(Jr T ∗) lifting 1-forms from n-manifolds to Jr T ∗. As an application we prove that for r ≥ 1 there is no canonical symplectic structure on Jr T ∗. We also solve similar problems with Jr ( ∧p T ∗), Jr (⊙p T ∗) and Jr (⊗p T ∗) playing the role of Jr T ∗.
منابع مشابه
Liftings of vector fields to 1-forms on the r-jet prolongation of the cotangent bundle
For natural numbers r and n ≥ 2 all natural operators T|Mfn T ∗(JrT ∗) transforming vector fields from n-manifolds M into 1-forms on JT ∗M = {j x(ω) | ω ∈ Ω(M), x ∈ M} are classified. A similar problem with fibered manifolds instead of manifolds is discussed.
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