### Higher order absolute differentiation with respect to generalized connections

Ivan Kolář (1984)

Banach Center Publications

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Ivan Kolář (1984)

Banach Center Publications

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Ivan Kolář (1971)

Czechoslovak Mathematical Journal

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Bohumil Cenkl (1967)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Ivan Kolář (1974)

Czechoslovak Mathematical Journal

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Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We describe all bundle functors G admitting natural operators transforming rth order holonomic connections on a fibered manifold Y → M into rth order holonomic connections on GY → M. For second order holonomic connections we classify all such natural operators.

Juraj Virsik (1971)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Anna Bednarska (2012)

Annales UMCS, Mathematica

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We prove that any first order F2 Mm1,m2,n1,n2-natural operator transforming projectable general connections on an (m1,m2, n1, n2)-dimensional fibred-fibred manifold p = (p, p) : (pY : Y → Y) → (pM : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on V Y → M.