×
Kurek, Jan; Mikulski, Włodzimierz M.

The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds. (English) Zbl 1116.58003

Cent. Eur. J. Math. 2, No. 5, 801-810 (2004).
An earlier result from [W. M. Mikulski, Arch. Math. Brno 31, No. 1, 1–7 (1995; Zbl 0837.53021)] is extended from manifolds to fibered manifolds. Namely, the authors determine all natural functions \(g:T^*(J^{(r,s, q)}(Y,\mathbf{R}^{1,1})_0)^*\to \text\textbf{R}\), for arbitrary fibered manifolds \(Y\) with \(m\)-dimensional base and \(n\)-dimensional fiber, for natural numbers \(r,s,q,m,n\) such that \(s\geq r\leq q\). Further, for natural numbers \(r,s,m,n\) with \(s\geq r\), all natural functions \(g:T^*(J^{(r,s)}(Y,\mathbf{R})_0)^*\to\text\textbf{R}\), are determined as well.
Reviewer: Vladimir Balan (Bucureşti)

MSC:

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

Keywords:

bundle functor; natural function

Citations:

Zbl 0837.53021
Cite Review PDF
Full Text: DOI
Creative Commons CC license icon Creative Commons BY license icon Creative Commons NC license icon Creative Commons ND license icon

References:

[1] M. Doupovec and J. Kurek: “Torsions of connections on higher order cotangent bundles”, Czechoslovak Math. J., Vol. 53(4), (2003), pp. 949-962. http://dx.doi.org/10.1023/B:CMAJ.0000024533.75199.eb; · Zbl 1080.53020
[2] I. Kolář: “On cotangent bundles of some natural bundles”, Supl. Rendiconti Circolo Math. Palermo, Vol. 37(II), (1994), pp. 115-120.; · Zbl 0839.58007
[3] I. Kolář, P. Michor and J. Slovák: Natural operations in differential geometry, Springer-Verlag, 1993.; · Zbl 0782.53013
[4] I. Kolář and W.M. Mikulski: “Contact elements on fibered manifolds”, Czechoslovak Math. J., Vol. 53(4), (2003) pp. 1017-1030. http://dx.doi.org/10.1023/B:CMAJ.0000024538.28153.47; · Zbl 1080.58002
[5] I. Kolář and M. Modugno: “Torsions of connections on some natural bundles”, Differential Geom. Appl., Vol. 2, (1992), pp. 1-16. http://dx.doi.org/10.1016/0926-2245(92)90006-9; · Zbl 0783.53021
[6] W.M. Mikulski: “Natural functions on T *T (r) and T *T r*” Arch. Math. Brno, Vol. 31(1), (1995), pp. 1-7.; · Zbl 0837.53021
[7] W.M. Mikulski: “Natural affinors on (J r,s,q (R 1,1)0)*”, Comment. Math. Univ. Carolinae, Vol. 42(4), (2001), pp. 655-663.; · Zbl 1090.58501
[8] A. Zajtz, “On the order of natural operators and liftings”, Ann. Polon. Math., Vol. 49, (1988), pp. 169-178.; · Zbl 0714.58059
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.