## Transformations of semiholonomic 2- and 3-jets and semiholonomic prolongation of connections.(English)Zbl 1213.53019

The natural transformations of semiholonomic jet functors $$\overline J^{r}$$ defined on the categories $$\mathcal Mf_{m} \times \mathcal Mf$$ and $$\mathcal{FM}_{m,n}$$ are described. Up to order three, exact coordinate formulae are known, for general order several related results are reminded. An application of semiholonomic jet transformations to prolongations of general connections is also shown. This work consists of the following parts: introduction; foundations; jets on the category $$\mathcal Mf_{m} \times \mathcal Mf$$; jet on the category $$\mathcal{FM}_{m,n}$$; prolongation of connections.

### MSC:

 53B05 Linear and affine connections 58A20 Jets in global analysis

### Keywords:

jet; natural transformation; connection; Ehresmann prolongation
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