The natural affinors on \((J^r T^{*,a})^*\). (English) Zbl 1050.58004

It is proved that for the \(r\)-th jet prolongation of the cotangent bundle \(J^rT^{*,a}M\) with negative weight \(a\), all natural affinors on its dual \((J^rT^{*,a}M)^*\) are constant multiples of the identity affinor whenever \(\dim M=n \geq 2\).


58A20 Jets in global analysis
53A55 Differential invariants (local theory), geometric objects
Full Text: EuDML


[1] Doupovec M.: Natural transformations between TTT*M and TT*TM. Czechoslovak Math. J. 43, 118 (1993), 599-613. · Zbl 0806.53024
[2] Doupovec M., Kolář I.: Natural affinors on time-dependent Weil bundles. Arch. Math. (Brno) 27 (1991), 205-209. · Zbl 0759.53007
[3] Gancarzewicz J., Kolář I.: Natural affinors on the extended r-th order tangent bundles. Suppl. Rendiconti Circolo Mat. Palermo 30 (1993), 95-100. · Zbl 0791.58009
[4] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry. Springer-Verlag, Berlin, 1993. · Zbl 0782.53013
[5] Kolář I., Modugno M.: Torsions of connections on some natural bundles. Diff. Geom. and Appl. 2 (1992), 1-16. · Zbl 0783.53021
[6] Kurek J.: Natural affinors on higher order cotangent bundles. Arch. Math. (Brno) 28 (1992), 175-180. · Zbl 0782.58007
[7] Mikulski W. M.: Natural affinors on r-jet prolongation of the tangent bundle. Arch. Math. (Brno) 34, 2 (1998), 321-328. · Zbl 0915.58006
[8] Mikulski W. M.: The natural affinors on (g>fcT(r). Note di Matematica, to appear. · Zbl 1008.58005
[9] Mikulski W. M.: The natural affinors on (JrT*)*. Arch. Math. (Brno) 36, 4 (2000), 261-267. · Zbl 1049.58012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.