Geodesic
The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 247-256
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We prove that every natural affinor on $(J^r( \odot ^2 T^{\ast }))^{\ast }(M)$ is proportional to the identity affinor if dim$M\ge 3$.
We prove that every natural affinor on $(J^r( \odot ^2 T^{\ast }))^{\ast }(M)$ is proportional to the identity affinor if dim$M\ge 3$.
Classification : 58A20, 58A32
Keywords: natural affinor; natural bundle; natural transformation 
@article{ARM_2003_39_3_a9,
     author = {Michalec, Pawe{\l}},
     title = {The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$},
     journal = {Archivum mathematicum},
     pages = {247--256},
     year = {2003},
     volume = {39},
     number = {3},
     mrnumber = {2010725},
     zbl = {1112.58300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a9/}
}
TY  - JOUR
AU  - Michalec, Paweł
TI  - The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$
JO  - Archivum mathematicum
PY  - 2003
SP  - 247
EP  - 256
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a9/
LA  - en
ID  - ARM_2003_39_3_a9
ER  - 
%0 Journal Article
%A Michalec, Paweł
%T The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$
%J Archivum mathematicum
%D 2003
%P 247-256
%V 39
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a9/
%G en
%F ARM_2003_39_3_a9
Michalec, Paweł. The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$. Archivum mathematicum, Tome 39 (2003) no. 3, pp. 247-256. http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a9/

[1] Doupovec M., Kolář I.: Natural affinors on time-dependent Weil bundles. Arch. Math. (Brno) 27 (1991), 205-209. | MR

[2] Doupovec M., Kurek J.: Torsions of connections of higher order cotangent bundles. Czech. Math. J. (to appear). | MR

[3] Gancarzewicz J., Kolář I.: Natural affinors on the extended $r$-th order tangent bundles. Suppl. Rendiconti Circolo Mat. Palermo, 1993, 95-100. | MR

[4] Kolář I., Modugno M.: Torsion of connections on some natural bundles. Diff. Geom. and Appl. 2(1992), 1-16. | MR

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

[6] Kurek J.: Natural affinors on higher order cotangent bundles. Arch. Math. (Brno) 28 (1992), 175-180. | MR

[7] Mikulski W. M.: The natural affinors on dual r-jet prolongation of bundles of 2-forms. Ann. UMCS Lublin 2002, (to appear). | MR

[8] Mikulski W. M.: Natural affinors on $r$-jet prolongation of the tangant bundle. Arch. Math. (Brno) 34 (2) (1998). 321-328. | MR

[9] Mikulski W. M.: The natural affinors on $ \otimes ^k T^{(k)}$. Note di Matematica vol. 19-n. 2. (1999), 269-274. | MR

[10] Mikulski W. M.: The natural affinors on generalized higher order tangent bundles. Rend. Mat. Roma vol. 21. (2001). (to appear). | MR | Zbl

[11] Mikulski W. M.: Natural affinors on $(J^{r,s,q}(\cdot ,{\bold R}^{1,1})_0)^\ast $. Coment. Math. Carolinae 42 (2001), (to appear). | MR | Zbl

[12] Zajtz A.: On the order of natural operators and liftings. Ann. Polon. Math. 49 (1988), 169-178. | MR