The natural operators lifting 1-forms to some vector bundle functors
نویسندگان
چکیده
منابع مشابه
The natural operators lifting 1 - forms to the r - jet prolongation of the cotangent bundle 1
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 ...
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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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Let r; n be xed natural numbers. We prove that for n-manifolds the set of all linear natural operators T ! T T (r) is a nitely dimensional vector space over R. We construct explicitly the bases of the vector spaces. As a corollary we nd all linear natural operators T ! T r. All manifolds and maps are assumed to be innnitely diierentiable. 0. Let r; n be xed natural numbers. Given a manifold M w...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2002
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm93-2-5