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1
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Natural transformations of the composition of Weil and cotangent functors

100%
Doupovec M.
Annales Polonici Mathematici
|
2001
|
tom 77
|
nr 2
105-117
EN
We study geometrical properties of natural transformations $T^{A}T* → T*T^{A}$ depending on a linear function defined on the Weil algebra A. We show that for many particular cases of A, all natural transformations $T^{A}T* → T*T^{A}$ can be described in a uniform way by means of a simple geometrical construction.
2
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Natural transformations between T²₁T*M and T*T²₁M

100%
Doupovec M.
Annales Polonici Mathematici
|
1991-1992
|
tom 56
|
nr 1
67-77
EN
We determine all natural transformations T²₁T*→ T*T²₁ where $T^r_k M = J^r_0 (ℝ^k,M)$. We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.
3
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Torsions of connections on time-dependent Weil bundles

100%
Doupovec M.
Colloquium Mathematicum
|
2003
|
tom 95
|
nr 1
53-62
EN
We introduce the concept of a dynamical connection on a time-dependent Weil bundle and we characterize the structure of dynamical connections. Then we describe all torsions of dynamical connections.
4
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Non-existence of exchange transformations of iterated jet functors

64%
Doupovec M., Mikulski W.
Banach Center Publications
|
2007
|
tom 76
|
nr 1
497-504
EN
We study the problem of the non-existence of natural transformations $J^{r}J^{s}Y → J^{s}J^{r}Y$ of iterated jet functors depending on some geometric object on the base of Y.
5
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On iteration of higher order jets and prolongation of connections

64%
Doupovec M., Mikulski W.
Annales Polonici Mathematici
|
2011
|
tom 100
|
nr 1
55-75
EN
We introduce exchange natural equivalences of iterated nonholonomic, holonomic and semiholonomic jet functors, depending on a classical linear connection on the base manifold. We also classify some natural transformations of this type. As an application we introduce prolongation of higher order connections to jet bundles.
6
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On prolongation of higher order connections

64%
Doupovec M., Mikulski W.
Annales Polonici Mathematici
|
2011
|
tom 102
|
nr 3
279-292
EN
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.
7
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On involutions of iterated bundle functors

64%
Doupovec M., Mikulski W.
Colloquium Mathematicum
|
2006
|
tom 106
|
nr 1
135-145
EN
We introduce the concept of an involution of iterated bundle functors. Then we study the problem of the existence of an involution for bundle functors defined on the category of fibered manifolds with m-dimensional bases and of fibered manifold morphisms covering local diffeomorphisms. We also apply our results to prolongation of connections.
8
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Gauge natural constructions on higher order principal prolongations

64%
Doupovec M., Mikulski W.
Annales Polonici Mathematici
|
2007
|
tom 92
|
nr 1
87-97
EN
Let $W^r_mP$ 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 $W^r_mP → M$. We also describe all geometric constructions of classical linear connections on $W^r_mP$ from principal connections on P → M and rth order linear connections on M.
9
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Gauge natural prolongation of connections

64%
Doupovec M., Mikulski W.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 1
37-50
EN
The main result is the classification of all gauge bundle functors H on the category $𝓟ℬ_m(G)$ which admit gauge natural operators transforming principal connections on P → M into general connections on HP → M. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to HP → P. A special attention is paid to linear connections.
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