Calcul différentiel extérieur de dégré arbitraire.
Calculus of variations with differential forms
We study integrals of the form , where , is continuous and is a -form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.
Calibrated geometries in Grassmann manifolds.
Canonical 1-forms on higher order adapted frame bundles
Let be a foliated -dimensional manifold with -dimensional foliation . Let be a finite dimensional vector space over . We describe all canonical (-invariant) -valued -forms on the -th order adapted frame bundle of .
Canonical differential structures of regular covectors
Canonical equivariant extensions using classical Hodge theory.
Canonical form on a groupoid related to regular prolongations of Lie groups
Canonical nonlinear connections in the multi-time Hamilton geometry.
Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.
We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σrk=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.
Canonical tensor fields of type (p,0) on Weil bundles
We give a classification of canonical tensor fields of type (p,0) on an arbitrary Weil bundle over n-dimensional manifolds under the condition that n ≥ p. Roughly speaking, the result we obtain says that each such canonical tensor field is a sum of tensor products of canonical vector fields on the Weil bundle.
Canonical vector valued 1-forms on higher order adapted frame bundles over category of fibered squares
Let Y be a fibered square of dimension (m1, m2, n1, n2). Let V be a finite dimensional vector space over. We describe all 21,m2,n1,n2 - canonical V -valued 1-form Θ TPrA (Y) → V on the r-th order adapted frame bundle PrA(Y).
Cartan geometry, supergravity and group manifold approach
We make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of classical gauge theory, as a background for understanding gauge theories of gravity in terms of Cartan geometry. The second part introduces the basics of the group manifold approach to supergravity, hinting at the deep rooted connections to Cartan supergeometry....
Categorical differential geometry
Certain relation between vector fields and distributions on a differentiable manifold
Certaines identifications dans les espaces de jets.
Champs de vecteurs et formes différentielles sur une variété des points proches
Let be a smooth manifold, a local algebra in sense of André Weil, the manifold of near points on of kind and the module of vector fields on . We give a new definition of vector fields on and we show that is a Lie algebra over . We study the cohomology of -differential forms. Résumé. On considère une variété différentielle, une algèbre locale au sens d’André Weil, la variété des points proches de d’espèce et le module des champs de vecteurs sur . On donne une nouvelle...
Champs totalement radiaux sur une structure de Thom-Mather
Dans la première partie de ce travail, on prouve l’existence de champs stratifiés dits totalement radiaux sur un ensemble stratifié abstrait (e.s.a.). Ces champs sont stables et peuvent être choisis continus sur les espaces stratifiés plongés qui sont -réguliers au sens de K. Bekka. Dans la seconde partie, on établit pour ces espaces un théorème de Poincaré-Hopf pour les champs totalement radiaux continus. On en déduit un résultat similaire pour les e.s.a.
Characterisations of Finetely Determined Equivariant Map Germs.
Characteristic Homomorphisms of Regular Lie Algebroids
Characteristic vector fields of generic distributions of corank 2