# Natural maps depending on reductions of frame bundles

@article{Kol2011NaturalMD, title={Natural maps depending on reductions of frame bundles}, author={Ivan Kol{\'a}ř}, journal={Annales Polonici Mathematici}, year={2011}, volume={102}, pages={83-90} }

We clarify how the natural transformations of fiber product
preserving bundle functors on the category of fibered manifolds
with m-dimensional bases and fiber preserving maps with local
diffeomorphisms as base maps can be constructed by using
reductions of the r-th order frame bundle of the base.

## 2 Citations

ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS

- Mathematics
- 2015

Abstract. We ﬁnd all FM m -natural operators Atransforming torsionfree classical linear connections ∇on m-manifolds M into base preservingﬁbred maps A(∇) : J r Y → J r Y for FM m -objects Y with…

## References

SHOWING 1-9 OF 9 REFERENCES

Iteration of Fiber Product Preserving Bundle Functors

- Mathematics
- 2001

Abstract. Using the theory of Weil algebras, we describe the composition of two product preserving bundle functors on the category of fibered manifolds with m-dimensional bases and fiber preserving…

On the fiber product preserving bundle functors

- Mathematics
- 1999

Ahsmrc~t: We present a complete description of all fiber product preserving bundle functc’rs on the category of tibered manifolds with m-dimensional bases and fiber preservin g maps with local…

Higher order jet involution

- Mathematics
- 2007

We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of…

Torsion-free connections on higher order frame bundles

- Mathematics
- 1996

We deduce that torsion-free connections on the r-th order frame bundle P r M of a manifold M can be identified with certain reductions of P r+1 M. They are also interpreted as splittings of T*M into…

HIGHER ORDER LINEAR CONNECTIONS FROM FIRST ORDER ONES

- Mathematics
- 2007

We describe how find all Mfm-natural operators D transforming torsion free classical linear connections ∇ on m-manifolds M into r-th order linear connections D(∇) on M.

Natural operations in differential geometry

- Mathematics
- 1993

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.…

Natural maps on the iterated jet prolongation of a fibred manifold

- Mathematics
- 1991

SummaryUsing an analytic procedure by the first author [5, 6], we first determine all natural transformations of the second iterated jet prolongation J1J1Y of a fibred manifold Y→X into itself…