Projective Connections in CR Geometry.
Projective limits of Banach vector bundles.
Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group.
Projectively flat Finsler metrics with orthogonal invariance
We study Finsler metrics with orthogonal invariance. By determining an expression of these Finsler metrics we find a PDE equivalent to these metrics being locally projectively flat. After investigating this PDE we manufacture projectively flat Finsler metrics with orthogonal invariance in terms of error functions.
Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.
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 natural bundles
Prolongation of pairs of connections into connections on vertical bundles
Let be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the -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 -vertical bundles. We also present some examples and applications.
Prolongation of Poisson -form on Weil bundles
In this paper, denotes a smooth manifold of dimension , a Weil algebra and the associated Weil bundle. When is a Poisson manifold with -form , we construct the -Poisson form , prolongation on of the -Poisson form . We give a necessary and sufficient condition for that be an -Poisson manifold.
Prolongation of projectable tangent valued forms
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
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 . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a -field for another Weil algebra and of its -prolongation.
Prolongation of tangent valued forms to Weil bundles
We prove that the so-called complete lifting of tangent valued forms from a manifold to an arbitrary Weil bundle over 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.
Prolongation of vector fields to jet bundles
[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.
Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de
Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of , we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz’s “regular separation” or Whitney’s “property (P)”.
Prolongement des champs de vecteurs à des variétés de points proches
Prolongement des courants, positifs, fermés de masse finie.
Prolongement des solutions holomorphes de problèmes aux limites
Dans cet article, on démontre, par des techniques d’analyse microlocale analytique, un résultat local de prolongement holomorphe pour les solutions de problèmes aux limites. Afin de minimiser le domaine dans lequel on suppose holomorphes au départ ces solutions, un résultat préliminaire de prolongement pour les solutions d’équations aux dérivées partielles a été obtenu, par la technique des déformations non caractéristiques, utilisant un théorème de Zerner dont on donne ici une nouvelle démonstration....
Prolongement des structures spinorielles sur la variété des jets
Prolongements d'équations différentielles linéaires. III. La suite exacte de cohomologie de Spencer
Propagation de singularités pour les opérateurs du type
Propagation des ondes dans les variétés à coins