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Functorial prolongations of Lie groupoids

100%

Kolář I.

Banach Center Publications

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2007

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tom 76

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nr 1

177-184

EN

For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.

2

Natural maps depending on reductions of frame bundles

100%

Kolář I.

Annales Polonici Mathematici

|

2011

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tom 102

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nr 1

83-90

EN

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.

3

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Higher order absolute differentiation with respect to generalized connections

100%

Kolář I.

Banach Center Publications

|

1984

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tom 12

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nr 1

153-161

4

On the torsion of linear higher order connections

100%

Kolář I.

Open Mathematics

|

2003

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tom 1

|

nr 3

360-366

EN

For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

5

The Frölicher-Nijenhuis bracket on some functional spaces

64%

Kolář I., Modungo M.

Annales Polonici Mathematici

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1998

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tom 68

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nr 2

97-106

EN

Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as $C^{∞}(E₁ₓ,E₂ₓ)$, for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated covariant differential and curvature.

6

On the absolute differentiation of geometric object fields

44%

Kolář I.

Annales Polonici Mathematici

|

1972-1973

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tom 27

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nr 3

293-304

7

On the reducibility of connections on the prolongations of vector bundles

44%

Kolář I.

Colloquium Mathematicum

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1974

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tom 30

|

nr 2

245-257

8

Lie derivatives of sectorform fields

32%

Kolář I.

Colloquium Mathematicum

|

1988

|

tom 55

|

nr 1

71-78

Ograniczanie wyników

3 Annales Polonici Mathematici

2 Banach Center Publications

2 Colloquium Mathematicum

1 Open Mathematics

8 Kolář I.

1 Modungo M.

1 2011

1 2007

1 2003

1 1998

1 1988

1 1984

1 1974

1 1973

Functorial prolongations of Lie groupoids

Natural maps depending on reductions of frame bundles

Higher order absolute differentiation with respect to generalized connections

On the torsion of linear higher order connections

The Frölicher-Nijenhuis bracket on some functional spaces

On the absolute differentiation of geometric object fields

On the reducibility of connections on the prolongations of vector bundles

Lie derivatives of sectorform fields