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Natural operations in differential geometry
I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.
On the natural operators on vector fields
We determine all natural operators transforming every vector field on a manifold M into a vector field on FM, where F is any natural bundle corresponding to a product preserving functor.This research
Natural operators related with the variational calculus
The Euler and Poincare-Cartan morphisms of the variational calculus in fibered manifolds are characterized from the naturality point of view.
Bundle functors of the jet type
Abstract. We introduce the general concept of jet functor on the product category Mf*Mf. We describe the extensions of jet functors to the category of fibered manifolds with m-dimensional bases and
Affine structure on Weil bundles
  • I. Kolář
  • Mathematics
    Nagoya Mathematical Journal
  • 1 June 2000
Abstract For every r-th order Weil functor TA , we introduce the underlying k-th order Weil functors We deduce that is an affine bundle for every manifold M. Generalizing the classical concept of
On the Helmholtz operator for Euler morphisms
The variational sequence describes the Helmholtz conditions for local variationality in terms of the Helmholtz map, which is defined on a factor space. We study a tensor modification of this
Higher order torsions of spaces with Cartan connection
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