Geodesic
Natural $T$-functions on the cotangent bundle of a Weil bundle
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 869-882
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A natural $T$-function on a natural bundle $F$ is a natural operator transforming vector fields on a manifold $M$ into functions on $FM$. For any Weil algebra $A$ satisfying $\dim M \ge {\mathrm width}(A)+1$ we determine all natural $T$-functions on $T^*T^AM$, the cotangent bundle to a Weil bundle $T^AM$.
A natural $T$-function on a natural bundle $F$ is a natural operator transforming vector fields on a manifold $M$ into functions on $FM$. For any Weil algebra $A$ satisfying $\dim M \ge {\mathrm width}(A)+1$ we determine all natural $T$-functions on $T^*T^AM$, the cotangent bundle to a Weil bundle $T^AM$.
Classification : 58A05, 58A20, 58A32
Keywords: natural bundle; natural operator; Weil bundle 
@article{CMJ_2004_54_4_a3,
     author = {Tom\'a\v{s}, Ji\v{r}{\'\i}},
     title = {Natural $T$-functions on the cotangent bundle of a {Weil} bundle},
     journal = {Czechoslovak Mathematical Journal},
     pages = {869--882},
     year = {2004},
     volume = {54},
     number = {4},
     mrnumber = {2100000},
     zbl = {1080.58001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a3/}
}
TY  - JOUR
AU  - Tomáš, Jiří
TI  - Natural $T$-functions on the cotangent bundle of a Weil bundle
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 869
EP  - 882
VL  - 54
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a3/
LA  - en
ID  - CMJ_2004_54_4_a3
ER  - 
%0 Journal Article
%A Tomáš, Jiří
%T Natural $T$-functions on the cotangent bundle of a Weil bundle
%J Czechoslovak Mathematical Journal
%D 2004
%P 869-882
%V 54
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a3/
%G en
%F CMJ_2004_54_4_a3
Tomáš, Jiří. Natural $T$-functions on the cotangent bundle of a Weil bundle. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 869-882. http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a3/

[1] R. J. Alonso: Jet manifold associated to a Weil bundle. Arch. Math. 36 (2000), 195–199. | MR | Zbl

[2] I.  Kolář: Covariant approach to natural transformations of Weil functors. Comm. Math. Univ. Carolin. 27 (1986), 723–729. | MR

[3] I. Kolář: On cotagent bundles of some natural bundles. Rend. Circ. Mat. Palermo. Serie II 37 (1994), 115–120. | MR

[4] I. Kolář: On the natural operators on vector fields. Ann. Global Anal. Geometry 6 (1988), 109–117. | DOI | MR

[5] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry. Springer-Verlag, , 1993. | MR

[6] I.  Kolář and Z. Radziszewski: Natural transformations of second tangent and cotangent bundles. Czechoslovak Math.  J. 38(113) (1988), 274–279. | MR

[7] W. M. Mikulski: The natural operators lifting vector fields to generalized higher order tangent bundles. Arch. Math. 36 (2000), 207–212. | MR | Zbl

[8] W. M. Mikulski: The jet prolongations of fibered fibered manifolds and the flow operator. Publ. Math. Debrecen 59 (2000), 441–458. | MR

[9] W. M.  Mikulski: The natural operators lifting vector fields to $(J^r T^* )^*$. Arch. Math. 36 (2000), 255–260. | MR | Zbl

[10] M. Modugno and G. Stefani: Some results on second tangent and cotangent spaces. Quaderni dell’Università di Lecce (1978), .

[11] F. J. Muriel, J. Munoz and J. Rodriguez: Weil bundles and jet spaces. Arch. Math. (to appear). | MR

[12] J. Tomáš: Natural operators on vector fields on the cotangent bundles of the bundles of $(k,r)$-velocities. Rend. Circ. Mat. Palermo II-54 (1998), 113–124. | MR | Zbl

[13] J.  Tomáš: Natural $T$-functions on the cotangent bundles bundles of some Weil bundles. Differential Geometry and Applications. Proc. of the Satellite Conf. of ICM in Berlin, Brno, August 10–14, 1998, 1998, pp. 293–302. | MR

[14] J.  Tomáš: On quasijet bundles. Rend. Circ. Mat. Palermo. Serie II 63 (2000), 187–196. | MR