Previous |  Up |  Next

Article

Title: The natural operators lifting connections to higher order cotangent bundles (English)
Author: Mikulski, Włodzimierz M.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 64
Issue: 2
Year: 2014
Pages: 509-518
Summary lang: English
.
Category: math
.
Summary: We prove that the problem of finding all ${\mathcal {M} f_m}$-natural operators ${C\colon Q\rightsquigarrow QT^{r*}}$ lifting classical linear connections $\nabla $ on $m$-manifolds $M$ into classical linear connections $C_M(\nabla )$ on the $r$-th order cotangent bundle $T^{r*}M=J^r(M,\mathbb R )_0$ of $M$ can be reduced to the well known one of describing all $\mathcal {M} f_m$-natural operators $D\colon Q\rightsquigarrow \bigotimes ^pT\otimes \bigotimes ^qT^*$ sending classical linear connections $\nabla $ on $m$-manifolds $M$ into tensor fields $D_M(\nabla )$ of type $(p,q)$ on $M$. (English)
Keyword: classical linear connection
Keyword: natural operator
MSC: 53C05
MSC: 58A20
MSC: 58A32
idZBL: Zbl 06391509
idMR: MR3277751
DOI: 10.1007/s10587-014-0116-7
.
Date available: 2014-11-10T09:54:46Z
Last updated: 2016-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/144013
.
Reference: [1] Dębecki, J.: Affine liftings of torsion-free connections to Weil bundles.Colloq. Math. 114 (2009), 1-8. MR 2457274, 10.4064/cm114-1-1
Reference: [2] Gancarzewicz, J.: Horizontal lift of connections to a natural vector bundle.Differential Geometry Proc. 5th Int. Colloq., Santiago de Compostela, Spain, 1984, Res. Notes Math. 131 Pitman, Boston (1985), 318-341 L. A. Cordero. Zbl 0646.53028, MR 0864879
Reference: [3] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. I.Interscience Publishers, New York (1963). Zbl 0119.37502, MR 0152974
Reference: [4] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Berlin (1993). MR 1202431
Reference: [5] Kurek, J., Mikulski, W. M.: The natural operators lifting connections to tensor powers of the cotangent bundle.Miskolc Math. Notes 14 (2013), 517-524. MR 3144087
Reference: [6] Kureš, M.: Natural lifts of classical linear connections to the cotangent bundle.J. Slovák Proc. of the 15th Winter School on geometry and physics, Srní, 1995, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43 (1996), 181-187. Zbl 0905.53018, MR 1463520
Reference: [7] Mikulski, W. M.: The natural bundles admitting natural lifting of linear connections.Demonstr. Math. 39 (2006), 223-232. Zbl 1100.58001, MR 2223893
.

Files

Files Size Format View
CzechMathJ_64-2014-2_16.pdf 232.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo