Displaying similar documents to “Natural transformations of separated jets”

Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *

Włodzimierz M. Mikulski (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let r , s , q , m , n ∈ ℕ be such that s ≥ r ≤ q . Let Y be a fibered manifold with m -dimensional basis and n -dimensional fibers. All natural affinors on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are classified. It is deduced that there is no natural generalized connection on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * . Similar problems with ( J r , s ( Y , ℝ ) 0 ) * instead of ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are solved.

Natural transformations of semi-holonomic 3-jets

Gabriela Vosmanská (1995)

Archivum Mathematicum

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Let J ¯ 3 be the functor of semi-holonomic 3 -jets and J ¯ 3 , 2 be the functor of those semi-holonomic 3 -jets, which are holonomic in the second order. We deduce that the only natural transformations J ¯ 3 → J ¯ 3 are the identity and the contraction. Then we determine explicitely all natural transformations J ¯ 3 , 2 → J ¯ 3 , 2 , which form two 5 -parameter families.

Natural maps depending on reductions of frame bundles

Ivan Kolář (2011)

Annales Polonici Mathematici

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We clarify how the natural transformations of fiber product preserving bundle functors on ℱ ℳ m can be constructed by using reductions of the rth order frame bundle of the base, ℱ ℳ m being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.

Non-existence of some canonical constructions on connections

Włodzimierz M. Mikulski (2003)

Commentationes Mathematicae Universitatis Carolinae

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For a vector bundle functor H : ℳ f → 𝒱 ℬ with the point property we prove that H is product preserving if and only if for any m and n there is an ℱ ℳ m , n -natural operator D transforming connections Γ on ( m , n ) -dimensional fibered manifolds p : Y → M into connections D ( Γ ) on H p : H Y → H M . For a bundle functor E : ℱ ℳ m , n → ℱ ℳ with some weak conditions we prove non-existence of ℱ ℳ m , n -natural operators D transforming connections Γ on ( m , n ) -dimensional fibered manifolds Y → M into connections D ( Γ ) on E Y → M .

Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski (2010)

Annales Polonici Mathematici

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Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an ℱ ℳ m , n -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.