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natural bundle; natural transformation
A classification of natural transformations transforming vector fields on $n$-manifolds into affinors on the extended $r$-th order tangent bundle over $n$-manifolds is given, provided $n\ge 3$.
[1] Gancarzewicz, J., Kolář, I.: Natural affinors on the extended $r$-th order tangent bundles. Winter school of Geometry and Physics, Srni 1991, Supl. Rendiconti Circolo Mat. Palermo, in press.
[2] Kolář, I., Slovák, J.: On the geometric functors on manifolds. Proceedings of the Winter school on Geometry and Physics, Srni 1988, Supl, Rendiconti Circolo Mat. Palermo (21) 1989, 223-233. MR 1009575
[3] Kolář., I., Vosmanská, G.: Natural transformations of higher order tangent bundles and jet spaces. Čas. pěst. mat. 114 (1989), 181-186. MR 1063764
[4] Mikulski, W. M.: Natural transformations transforming functions and vector fields to functions on some natural bundles. Mathematica Bohemica 117 (1992), 217-223. MR 1165899 | Zbl 0810.58004
[5] Mikulski, W. M.: Some natural operations on vector fields. Rendiconti di Matematica (Roma) VII (12) (1992), 783-803. MR 1205977 | Zbl 0766.58005
[6] Nijenhuis, A.: Natural bundles and their general properties. in Differential Geometry in Honor of K. Yano, Kinokuniya (Tokyo) (1972), 317-343. MR 0380862 | Zbl 0246.53018
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