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Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.

Jaime Muñoz Masqué (1985)

Revista Matemática Iberoamericana

The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...

Principal prolongations and geometries modeled on homogeneous spaces.

Slovák, J. (1996)

Archivum Mathematicum

Principal prolongations and geometries modeled on homogeneous spaces

Jan Slovák (1996)

Archivum Mathematicum

We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.

Problèmes de modules pour les formes différentielles singulières dans le plan complexe.

Paulo Sad, Dominique Cerveau (1986)

Commentarii mathematici Helvetici

Product preserving bundle functors on fibered fibered manifolds

Włodzimierz M. Mikulski, Jiří M. Tomáš (2003)

Colloquium Mathematicae

We investigate the category of product preserving bundle functors defined on the category of fibered fibered manifolds. We show a bijective correspondence between this category and a certain category of commutative diagrams on product preserving bundle functors defined on the category ℳ f of smooth manifolds. By an application of the theory of Weil functors, the latter category is considered as a category of commutative diagrams on Weil algebras. We also mention the relation with natural transformations...

Product preserving bundles on foliated manifolds

Włodzimierz M. Mikulski (2004)

Annales Polonici Mathematici

We present a complete description of all product preserving bundle functors on the category ℱol of all foliated manifolds and their leaf respecting maps in terms of homomorphisms of Weil algebras.

Product preserving gauge bundle functors on all principal bundle homomorphisms

Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means of Weil functors....

Projective limits of Banach vector bundles.

Galanis, G.N. (1998)

Portugaliae Mathematica

Prolongation of natural bundles

Anton Dekrét (1985)

Mathematica Slovaca

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.

Prolongement des structures spinorielles sur la variété des jets

Irina Ana Turtoi (1994)

Annales de l'I.H.P. Physique théorique

Currently displaying 1 – 15 of 15

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