Previous |  Up |  Next

# Article

Full entry | PDF   (0.2 MB)
Keywords:
natural affinor; jet prolongations
Summary:
We deduce that for $n\ge 2$ and $r\ge 1$, every natural affinor on $J^rT$ over $n$-manifolds is of the form $\lambda \delta$ for a real number $\lambda$, where $\delta$ is the identity affinor on $J^rT$.
References:
[1] Doupovec, M.: Natural transformations between $TTT^*M$ and $TT^*TM$. Czechoslovak Math. J. 43 (118) 1993, 599-613. MR 1258423 | Zbl 0806.53024
[2] Gancarzewicz, J., Kolář, I.: Natural affinors on the extended $r$-th order tangent bundles. Suppl. Rendiconti Circolo Mat. Palermo, 1993. MR 1246623
[3] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, Berlin, 1993. MR 1202431
[4] Kolář, I., Modugno, M.: Torsion of connections on some natural bundles. Diff. Geom. and Appl. 2 (1992), 1-16. MR 1244453
[5] Kurek, J.: Natural affinors on higher order cotangent bundles. Arch. Math. (Brno) 28 (1992), 175-180. MR 1222284
[6] Zajtz, A.: On the order of natural operators and liftings. Ann. Polon. Math. 49 (1988), 169-178. MR 0983220

Partner of