On lifting of connections to Weil bundles

Jan Kurek, and Włodzimierz M. Mikulski. "On lifting of connections to Weil bundles." Annales Polonici Mathematici 103.3 (2012): 319-324. <http://eudml.org/doc/280351>.

@article{JanKurek2012,
abstract = {We prove that the problem of finding all $ℳ f_m$-natural operators $B:Q⟿ QT^A$ lifting classical linear connections ∇ on m-manifolds M to classical linear connections $B_M(∇)$ on the Weil bundle $T^\{A\}M$ corresponding to a p-dimensional (over ℝ) Weil algebra A is equivalent to the one of finding all $ℳ f_m$-natural operators $C:Q ⟿ (T¹_\{p-1\},T* ⊗ T* ⊗ T)$ transforming classical linear connections ∇ on m-manifolds M into base-preserving fibred maps $C_M(∇):T¹_\{p-1\}M = ⨁^\{p-1\}_\{M\} TM → T*M ⊗ T*M ⊗ TM$.},
author = {Jan Kurek, Włodzimierz M. Mikulski},
journal = {Annales Polonici Mathematici},
keywords = {Weil algebra; Weil bundle; classical linear connection; natural operator},
language = {eng},
number = {3},
pages = {319-324},
title = {On lifting of connections to Weil bundles},
url = {http://eudml.org/doc/280351},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Jan Kurek
AU - Włodzimierz M. Mikulski
TI - On lifting of connections to Weil bundles
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 3
SP - 319
EP - 324
AB - We prove that the problem of finding all $ℳ f_m$-natural operators $B:Q⟿ QT^A$ lifting classical linear connections ∇ on m-manifolds M to classical linear connections $B_M(∇)$ on the Weil bundle $T^{A}M$ corresponding to a p-dimensional (over ℝ) Weil algebra A is equivalent to the one of finding all $ℳ f_m$-natural operators $C:Q ⟿ (T¹_{p-1},T* ⊗ T* ⊗ T)$ transforming classical linear connections ∇ on m-manifolds M into base-preserving fibred maps $C_M(∇):T¹_{p-1}M = ⨁^{p-1}_{M} TM → T*M ⊗ T*M ⊗ TM$.
LA - eng
KW - Weil algebra; Weil bundle; classical linear connection; natural operator
UR - http://eudml.org/doc/280351
ER -