Geodesic
Natural transformations of semi-holonomic 3-jets
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 313-318
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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.
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.
Classification : 53A55, 58A20
Keywords: semi-holonomic 3-jet; natural transformation 
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Vosmanská, Gabriela. Natural transformations of semi-holonomic 3-jets. Archivum mathematicum, Tome 31 (1995) no. 4, pp. 313-318. http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a8/

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