The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$
Michalec, Paweł
Archivum Mathematicum, Tome 039 (2003), p. 247-256 / Harvested from Czech Digital Mathematics Library
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We prove that every natural affinor on $(J^r( \odot ^2 T^{\ast }))^{\ast }(M)$ is proportional to the identity affinor if dim$M\ge 3$.

Publié le : 2003-01-01
Classification:  58A20,  58A32 
@article{107871,
     author = {Pawe\l\ Michalec},
     title = {The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$},
     journal = {Archivum Mathematicum},
     volume = {039},
     year = {2003},
     pages = {247-256},
     zbl = {1112.58300},
     mrnumber = {2010725},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107871}
}

Michalec, Paweł. The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$. Archivum Mathematicum, Tome 039 (2003) pp. 247-256. http://gdmltest.u-ga.fr/item/107871/

Doupovec M.; Kolář I. Natural affinors on time-dependent Weil bundles, Arch. Math. (Brno) 27 (1991), 205-209. (1991) | MR 1189217

Doupovec M.; Kurek J. Torsions of connections of higher order cotangent bundles, Czech. Math. J. (to appear). | MR 2018842

Gancarzewicz J.; Kolář I. Natural affinors on the extended $r$-th order tangent bundles, Suppl. Rendiconti Circolo Mat. Palermo, 1993, 95-100. (1993) | MR 1246623

Kolář I.; Modugno M. Torsion of connections on some natural bundles, Diff. Geom. and Appl. 2(1992), 1-16. (1992) | MR 1244453

Kolář. I.; Michor P. W.; Slovák J. Natural Operations in Differential Geometry, Springer-Verlag, Berlin 1993. (1993) | MR 1202431 | Zbl 0782.53013

Kurek J. Natural affinors on higher order cotangent bundles, Arch. Math. (Brno) 28 (1992), 175-180. (1992) | MR 1222284

Mikulski W. M. The natural affinors on dual r-jet prolongation of bundles of 2-forms, Ann. UMCS Lublin 2002, (to appear). | MR 1984608

Mikulski W. M. Natural affinors on $r$-jet prolongation of the tangant bundle, Arch. Math. (Brno) 34 (2) (1998). 321-328. (1998) | MR 1645340

Mikulski W. M. The natural affinors on $ \otimes ^k T^{(k)}$, Note di Matematica vol. 19-n. 2. (1999), 269-274. (19-n) | MR 1816880

Mikulski W. M. The natural affinors on generalized higher order tangent bundles, Rend. Mat. Roma vol. 21. (2001). (to appear). | MR 1884952 | Zbl 1048.58004

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 1883375 | Zbl 1050.58004

Zajtz A. On the order of natural operators and liftings, Ann. Polon. Math. 49 (1988), 169-178. (1988) | MR 0983220