Lie derivatives of sectorform fields
Higher order absolute differentiation with respect to generalized connections
On the torsion of linear higher order connections
For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.
On the reducibility of connections on the prolongations of vector bundles
Higher order torsions of spaces with Cartan connection
On special types of nonholonomic jets
An abstract characterization of the jet spaces
A general point of view to nonholonomic jet bundles
On the absolute differentiation of geometric object fields
Geometrie v současné matematice a její úloha ve vyučování
Zamyšlení nad diferenciálně geometrickým dílem Eduarda Čecha
Natural operations on higher order tangent bundles.
We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.
On the Weilian prolongations of natural bundles
We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration of two natural bundles and . Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.
Functorial prolongations of Lie groupoids
For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.
Natural maps depending on reductions of frame bundles
We clarify how the natural transformations of fiber product preserving bundle functors on can be constructed by using reductions of the rth order frame bundle of the base, being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.
On the natural transformations of Weil bundles
First we deduce some general results on the covariant form of the natural transformations of Weil functors. Then we discuss several geometric properties of these transformations, special attention being paid to vector bundles and principal bundles.
On special types of nonholonomic -jets
We deduce a classification of all special types of nonholonomic -jets. In the introductory part, we summarize the basic properties of nonholonomic -jets.
On the infinitesimal geometric objects of submanifolds
Higher order torsions of manifolds with connection
Natural transformations of the second tangent functor into itself
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