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Journals and Conferences
We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of r-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector… (More)
Using the description of a fiber product preserving bundle functor F in terms of Weil algebras, we deduce several geometric properties of the Fprolongations of principal and associated bundles. Then we clarify that the flow prolongation with respect to F of a projectable vector field can be constructed by using a natural morphism.
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms between our bundles of smooth maps, we introduce the concept of fiberwise (k, r)-jet. The relations to the EulerLagrange… (More)
We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration F (EM) of two natural bundles E and F . Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.
We deduce a classification of all special types of nonholonomic 3-jets. In the introductory part, we summarize the basic properties of nonholonomic r-jets. Generally speaking, a very attractive phenomenon of the problem of classifying the special types of nonholonomic 3-jets is that its solution is heavily based on the Weil algebra technique, even though no… (More)
We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector fields in both cases and we prove that the bracket is preserved. Our proof is based on several new results concerning the finite dimensional… (More)
In this paper we prove that each g-natural metric on a linear frame bundle LM over a Riemannian manifold (M, g) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define g-natural metrics on the orthonormal frame bundle OM and we prove the same invariance result as above for OM . Hence we see that, over a space (M,… (More)
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.
We study the prolongation of linear connections on a vector bundle E and of E-valued k-forms with respect to an arbitrary Weil functor T A. We present a practical algorithm for these procedures that is heavily based on the multiplication in the Weil algebra A. Our main theoretical result is that the covariant exterior differential of E-valued k-forms in the… (More)