The natural operators lifting connections to higher order cotangent bundles

Mikulski, Włodzimierz M.. "The natural operators lifting connections to higher order cotangent bundles." Czechoslovak Mathematical Journal 64.2 (2014): 509-518. <http://eudml.org/doc/262045>.

@article{Mikulski2014,
abstract = {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 $M$.},
author = {Mikulski, Włodzimierz M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {classical linear connection; natural operator; classical linear connection; natural operator},
language = {eng},
number = {2},
pages = {509-518},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The natural operators lifting connections to higher order cotangent bundles},
url = {http://eudml.org/doc/262045},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - The natural operators lifting connections to higher order cotangent bundles
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 509
EP - 518
AB - 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 $M$.
LA - eng
KW - classical linear connection; natural operator; classical linear connection; natural operator
UR - http://eudml.org/doc/262045
ER -