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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:
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