Automorphisms of differential groups
Automorphisms of spatial curves
Automorphisms of curves , in are investigated; i.e. invertible transformations, where the coordinates of the transformed curve , depend on the derivatives of the original one up to some finite order . While in the two-dimensional space the problem is completely resolved (the only possible transformations are the well-known contact transformations), the three-dimensional case proves to be much more complicated. Therefore, results (in the form of some systems of partial differential equations...
Automorphisms of submanifolds.
Bundle functors on all foliated manifold morphisms have locally finite order
We prove that any bundle functor F:ℱol → ℱℳ on the category ℱ olof all foliated manifolds without singularities and all leaf respecting maps is of locally finite order.
Bundle functors with the point property which admit prolongation of connections
Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.
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 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 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).
Certain relation between vector fields and distributions on a differentiable manifold
Certaines identifications dans les espaces de jets.
Characterisations of Finetely Determined Equivariant Map Germs.
Charles Ehresmann's concepts in differential geometry
We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.
Classification of principal connections naturally induced on
We consider a vector bundle and the principal bundle of frames of . Let be a principal connection on and let be a linear connection on . We classify all principal connections on naturally given by and .
Cohomology of the variational complex in the class of exterior forms of finite jet order.
Combinatorics of non-holonomous jets
Connections and 1-jet fiber bundles
Connections of higher order and product preserving functors
In this paper we consider a product preserving functor of order and a connection of order on a manifold . We introduce horizontal lifts of tensor fields and linear connections from to with respect to . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
Connections on 1-jets principal fiber bundles
Connections on higher order tangent bundles