The Category of Differential Triads
The constructions of general connections on second jet prolongation
We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M
The generic dimension of the first derived system
Any -dimensional subbundle of the cotangent bundle on an -dimensional manifold partitions into subsets ( being the minimum of and , the combinations of things taken 2 at a time). is the set on which the first derived systems of the subbundle has codimension .In this paper we prove the following:Theorem. Let and let be a generic -dimensional subbundle...
The natural affinors on some fiber product preserving gauge bundle functors of vector bundles
We classify all natural affinors on vertical fiber product preserving gauge bundle functors on vector bundles. We explain this result for some more known such . We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor dual to as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.
The natural transformations between T-th order prolongation of tangent and cotangent bundles over Riemannian manifolds
If (M,g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T* M given by v → g(v,−) between the tangent TM and the cotangent T* M bundles of M. In the present note first we generalize this isomorphism to the one JrTM → JrTM between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT M of cotangent TM bundles of M. Further we describe all base preserving vector bundle maps DM(g) : JrTM → JrT* M depending on a Riemannian...
The structure of smooth mappings over Weil algebras and the category of manifolds over algebras.
The tangent stars of a set, and extensions of smooth functions.
Topogical equivalence of monotone nonlinear nonautonomous differential equations
Travaux de D. Anosov et S. Smale sur les difféomorphismes
Travaux de Novikov sur les feuilletages