Liftings of functions and vector fields to natural bundles

Jacek Gancarzewicz

Displaying similar documents to “Liftings of functions and vector fields to natural bundles”

Lifting of linear vector fields to fiber product preserving vertical gauge bundles

J. Kurek, W. M. Mikulski (2005)

Colloquium Mathematicae

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We classify all natural operators lifting linear vector fields on vector bundles to vector fields on vertical fiber product preserving gauge bundles over vector bundles. We explain this result for some known examples of such bundles.

Natural operators lifting functions to affinors on higher order cotangent bundles

W. M. Mikulski (2004)

Annales Polonici Mathematici

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For natural numbers n ≥ 3 and r ≥ 1 all natural operators $A : T_{| ℳ f ₙ}^{(0, 0)} ⟿ T^{(1, 1)} T^{r *}$ transforming functions from n-manifolds into affinors (i.e. tensor fields of type (1,1)) on the r-cotangent bundle are classified.

Natural differential operators between some natural bundles

Włodzimierz M. Mikulski (1993)

Mathematica Bohemica

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Let $F$ and $G$ be two natural bundles over $n$ -manifolds. We prove that if $F$ is of type (I) and $G$ is of type (II), then any natural differential operator of $F$ into $G$ is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.

On cotangent bundles of some natural bundles

Kolář, Ivan

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The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle $F$ ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of $F$ . It is deduced that under certain assumptions on $F$ , all natural operators of the second type can be constructed through those of the first one.

Fibre bundles associated with fields of geometric objects and the structure tensor

J. J. Konderak (1991)

Annales Polonici Mathematici

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On the reducibility of connections on the prolongations of vector bundles

Ivan Kolář (1974)

Colloquium Mathematicae

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On oriented vector bundles over CW-complexes of dimension 6 and 7

Martin Čadek, Jiří Vanžura (1992)

Commentationes Mathematicae Universitatis Carolinae

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Necessary and sufficient conditions for the existence of $n$ -dimensional oriented vector bundles ( $n = 3, 4, 5$ ) over CW-complexes of dimension $\leq 7$ with prescribed Stiefel-Whitney classes $w_{2} = 0$ , $w_{4}$ and Pontrjagin class $p_{1}$ are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.

On Weil Bundles of the First Order

Adgam Yakhievich Sultanov (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The descriptions of Weil bundles, lifts of functions and vector fields are given. Actions of the automorphisms group of the Whitney sum of algebras of dual numbers on a Weil bundle of the first order are defined.

About $G$ -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

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Let $G$ be a complex algebraic group, simple and simply connected, $T$ a maximal torus and $W$ the Weyl group. One shows that the coarse moduli space $M_{G} (X)$ parametrizing $S$ -equivalence classes of semistable $G$ -bundles over an elliptic curve $X$ is isomorphic to $[Γ (T) \otimes_{Z} X] / W$ . By a result of Looijenga, this shows that $M_{G} (X)$ is a weighted projective space.

Trivial noncommutative principal torus bundles

Stefan Wagner (2011)

Banach Center Publications

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A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic...