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Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

Let A be a Weil algebra and V be an A-module with dimR V < ∞. Let E → M be a vector bundle and let TA,VE → TAM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form TA,Vφ : TA,V E → ΛpT*TAM ⊗­TAM TTA,VE on TA,VE → TAM from a linear semibasic tangent valued p-form φ : E → ΛpT*M ⊗­ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vφ, TA,Vψ]] = TA,V ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and...

Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec, Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to F -vertical bundles. We also present some examples and applications.

Prolongation of Poisson 2 -form on Weil bundles

Norbert Mahoungou Moukala, Basile Guy Richard Bossoto (2016)

Archivum Mathematicum

In this paper, M denotes a smooth manifold of dimension n , A a Weil algebra and M A the associated Weil bundle. When ( M , ω M ) is a Poisson manifold with 2 -form ω M , we construct the 2 -Poisson form ω M A A , prolongation on M A of the 2 -Poisson form ω M . We give a necessary and sufficient condition for that M A be an A -Poisson manifold.

Prolongation of projectable tangent valued forms

Antonella Cabras, Ivan Kolář (2002)

Archivum Mathematicum

First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.

Prolongation of second order connections to vertical Weil bundles

Antonella Cabras, Ivan Kolář (2001)

Archivum Mathematicum

We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra A . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a B -field for another Weil algebra B and of its A -prolongation.

Prolongation of tangent valued forms to Weil bundles

Antonella Cabras, Ivan Kolář (1995)

Archivum Mathematicum

We prove that the so-called complete lifting of tangent valued forms from a manifold M to an arbitrary Weil bundle over M preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.

Quantum homogeneous superspaces and quantum duality principle

Rita Fioresi (2015)

Banach Center Publications

We define the concept of quantum section of a line bundle of a homogeneous superspace and we employ it to define the concept of quantum homogeneous projective superspace. We also suggest a generalization of the QDP to the quantum supersetting.

Quaternionic contact structures in dimension 7

David Duchemin (2006)

Annales de l’institut Fourier

The conformal infinity of a quaternionic-Kähler metric on a 4 n -manifold with boundary is a codimension 3 distribution on the boundary called quaternionic contact. In dimensions 4 n - 1 greater than 7 , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7 , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures...

Quelques conséquences locales de la théorie de Hodge

François Loeser (1985)

Annales de l'institut Fourier

Un résultat de positivité de théorie de Hodge nous permet de déterminer certaines pôles de la distribution | f | 2 z pour f une fonction analytique à singularité isolée. Dans le cas des courbes et des singularités quasi-homogènes on détermine l’ensemble exact des pôles. On démontre aussi que si le résidu d’une forme holomorphe est de carré intégrable sur la fibre spéciale, l’intégrale sur la fibre spéciale est limite de celle sur les fibres voisines.

Currently displaying 801 – 820 of 1152