Geodesic
Natural transformations of semi-holonomic 3-jets
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 313-318 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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/

[1] Ehresmann, C.: Extension du calcul des jets aux jets non-holonomes. C.R.Acad. Sci. Paris, 239 (1954), 1762-1764. | MR | Zbl

[2] Kolř, I.: The contact of spaces with connection. J. Differential Geometry 7 (1972), 563-570. | MR

[3] Kolř, I., Michor, P., Slov k, J.: Natural Operations in Differential Geometry. Springer-Verlag, 1993. | MR

[4] Kolř, I., Vosmansk , G.: Natural operations with second order jets. Rendiconti del Circolo Matematico di Palermo, Serie II, n. 14 (1987), 179-186. | MR

[5] Kolř, I., Vosmansk , G.: Natural transformations of higher order tangent bundles and jet spaces. Čas. pěst. mat. 114 (1989), 181-186. | MR

[6] Virsik, G.: Total connections in Lie groupoids. Arch. Math. (Brno), 31 (1995), 183-200. | MR | Zbl