Let $\bar{J}^3$ be the functor of semi-holonomic $3$-jets and $\bar{J}^{3,2}$ be the functor of those semi-holonomic $3$-jets, which are holonomic in the second order. We deduce that the only natural transformations $\bar{J}^3 \rightarrow \bar{J}^3$ are the identity and the contraction. Then we determine explicitely all natural transformations $\bar{J}^{3,2}\rightarrow \bar{J}^{3,2}$, which form two $5$-parameter families.
@article{107553,
author = {Gabriela Vosmansk\'a},
title = {Natural transformations of semi-holonomic 3-jets},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {313-318},
zbl = {0852.58003},
mrnumber = {1390591},
language = {en},
url = {http://dml.mathdoc.fr/item/107553}
}
Vosmanská, Gabriela. Natural transformations of semi-holonomic 3-jets. Archivum Mathematicum, Tome 031 (1995) pp. 313-318. http://gdmltest.u-ga.fr/item/107553/
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