Displaying similar documents to “On the space of maps inducing isomorphic connections”

The generic dimension of the first derived system

Robert P. Buemi (1978)

Annales de l'institut Fourier

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Any r -dimensional subbundle of the cotangent bundle on an n -dimensional manifold M partitions M into subsets M 0 , ... , M m ( m being the minimum of r and C ( n - r , 2 ) , the combinations of n - r things taken 2 at a time). M i is the set on which the first derived systems of the subbundle has codimension i . In this paper we prove the following: Theorem. Let s ≥ 2 and let Q be a generic C s r -dimensional subbundle of the cotangent bundle of an n -dimensional manifold M . The codimension...

Gauge natural constructions on higher order principal prolongations

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

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Let W m r P be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on W m r P → M . We also describe all geometric constructions of classical linear connections on W m r P from principal connections on P → M and rth order linear connections on 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.

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 .

A construction of a connection on G Y → Y from a connection on Y → M by means of classical linear connections on M and Y

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a bundle functor of order ( r , s , q ) , s ≥ r ≤ q , on the category ℱ ℳ m , n of ( m , n ) -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection Γ on an ℱ ℳ m , n -object Y → M we construct a general connection 𝒢 ( Γ , λ , Λ ) on G Y → Y be means of an auxiliary q -th order linear connection λ on M and an s -th order linear connection Λ on Y . Then we construct a general connection 𝒢 ( Γ , ∇ 1 , ∇ 2 ) on G Y → Y by means of auxiliary classical linear connections ∇ 1 on M and ∇ 2 on Y . In the case G = J 1 we determine all general connections...

Canonical 1-forms on higher order adapted frame bundles

Jan Kurek, Włodzimierz M. Mikulski (2008)

Archivum Mathematicum

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Let ( M , ℱ ) be a foliated m + n -dimensional manifold M with n -dimensional foliation ℱ . Let V be a finite dimensional vector space over 𝐑 . We describe all canonical ( ℱ ol m , n -invariant) V -valued 1 -forms Θ : T P r ( M , ℱ ) → V on the r -th order adapted frame bundle P r ( M , ℱ ) of ( M , ℱ ) .