On lifting of connections to Weil bundles
Tom 103 / 2012
Annales Polonici Mathematici 103 (2012), 319-324
MSC: Primary 58A32; Secondary 58A20.
DOI: 10.4064/ap103-3-7
Streszczenie
We prove that the problem of finding all -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.
