We introduce the concept of modified vertical Weil functors on the category \mathcal{F}\mathcal{M}_m of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on \mathcal{F}\mathcal{M}_m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors T^{a} corresponding to Weil algebras A by the so called modified Weil functors T^{a} corresponding to Weil algebra bundle functors A on the category \mathcal{F}\mathcal{M}_m of m-dimensional manifolds and their embeddings., Włodzimierz M. Mikulski., and Obsahuje seznam literatury
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.
Let M be an m-dimensional manifold and A = Dr k/I = R⊕NA a Weil algebra of height r. We prove that any A-covelocity TA x f ∈ TA x M, x ∈ M is determined by its values over arbitrary max{widthA,m} regular and under the first jet projection linearly independent elements of TA x M. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result TA M ≃ T r M without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from m > k to all cases of m. We also introduce the space JA(M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space Jr(M,N)., Jiří Tomáš., and Seznam literatury