On lifting of connections to Weil bundles
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 319-324
MSC: Primary 58A32; Secondary 58A20.
DOI: 10.4064/ap103-3-7
Abstract
We prove that the problem of finding all $\mathcal M f_m$-natural operators $B:Q\rightsquigarrow QT^A$ lifting classical linear connections $\nabla$ on $m$-manifolds $M$ to classical linear connections $B_M(\nabla)$ on the Weil bundle $T^AM$ corresponding to a $p$-dimensional (over $\mathbb R$) Weil algebra $A$ is equivalent to the one of finding all $\mathcal M f_m$-natural operators $C:Q\rightsquigarrow (T^1_{p-1},T^*\otimes T^*\otimes T)$ transforming classical linear connections $\nabla$ on $m$-manifolds $M$ into base-preserving fibred maps $C_M(\nabla):T^1_{p-1}M=\bigoplus^{p-1}_MTM\to T^*M\otimes T^*M\otimes TM$.
