Product preserving bundle functors on fibered manifolds
The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given.
Product preserving bundle functors on multifibered and multifoliate manifolds.
Product preserving bundles on foliated manifolds
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
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....
Product preserving gauge bundle functors on vector bundles
A complete description is given of all product preserving gauge bundle functors F on vector bundles in terms of pairs (A,V) consisting of a Weil algebra A and an A-module V with . Some applications of this result are presented.
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...
Regular analytic arcs and curves
Regular and coregular mappings of differential spaces
Seven-dimensional considerations of Einstein's connection. II: The recurrence relations of the second and third kind in 7--UFT.
Seven-dimensional considerations of Einstein's connection. I: The recurrence relations of the first kind in --UFT.
Seven-dimensional considerations of Einstein'sconnection. III: The seven-dimensional Einstein's connection.
Six-dimensional considerations of Einstein's connection for the first two-classes. I: The recurrence relations in 6--UFT.
Smooth structures on fibre jet spaces
Splitting theorems for the double tangent bundles of Fréchet manifolds.
Strongly differentiable monoids with smooth boundary.
Structure morphisms of prolongation functors
Sur l'algèbre de Lie des sections d'un fibré en algèbres de Lie
On étudie la structure naturelle d’algèbre de Lie de l’espace des sections de classe d’un fibré localement trivial dont la fibre-type est une algèbre de Lie ; on décrit, en particulier, ses dérivations et ses automorphismes. On détermine les algèbres de Lie pour lesquelles cette structure caractérise la structure différentiable de la base du fibré.
Sur les crochets généralisés et quelques unes de leurs applications
Sur une famille de variétés à bord lipschitziennes. Application à un problème d'identification de domaines
étant un ouvert borné de donné, on considère l’ensemble des ouverts de inclus dans , localement uniformément image de demi-espaces par des homéomorphismes bilipschitiziens. Les cartes locales sont définies sur des boules de rayon , elles sont bilipschitziennes de constante .On montre que cette famille est plus générale que celle des ouverts uniformément lipschitziens.On montre ensuite en utilisant une méthode de réflexions que pour , les espaces de Sobolev
The Category of Differential Triads