On the natural operators of Bianchi type
On the natural operators transforming vector fields to the -th tensor power
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 the order of natural differential operators and liftings
On the Prolongations of Differentiable Distributions
On the reducibility of connections on the prolongations of vector bundles
On the structure function of a -structure
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 underlying lower order bundle functors
For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with -dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.
On the uniqueness of some differential invariants: , ,
On the variational calculus in fibered-fibered manifolds
In this paper we extend the variational calculus to fibered-fibered manifolds. Fibered-fibered manifolds are surjective fibered submersions π:Y → X between fibered manifolds. For natural numbers s ≥ r ≤ q with r ≥ 1 we define (r,s,q)th order Lagrangians on fibered-fibered manifolds π:Y → X as base-preserving morphisms . Then similarly to the fibered manifold case we define critical fibered sections of Y. Setting p=max(q,s) we prove that there exists a canonical “Euler” morphism of λ satisfying...
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.
On the -equivalence of semiholonomic jets
It is well known that the concept of holonomic -jet can be geometrically characterized in terms of the contact of individual curves. However, this is not true for the semiholonomic -jets, [5], [8]. In the present paper, we discuss systematically the semiholonomic case.
On third order semiholonomic prolongation of a connection
We recall several different definitions of semiholonomic jet prolongations of a fibered manifold and use them to derive some interesting properties of prolongation of a first order connection to a third order semiholonomic connection.
On Weil Bundles of the First Order
The descriptions of Weil bundles, lifts of functions and vector fields are given. Actions of the automorphisms group of the Whitney sum of algebras of dual numbers on a Weil bundle of the first order are defined.
Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles
Let be a principal bundle of frames with the structure group . It is shown that the variational problem, defined by -invariant Lagrangian on , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.
Orientability of higher order Grassmannians