Lifting to the r-frame bundle by means of connections

J. Kurek, and W. M. Mikulski. "Lifting to the r-frame bundle by means of connections." Annales Polonici Mathematici 97.1 (2010): 63-71. <http://eudml.org/doc/280755>.

@article{J2010,
abstract = {Let m and r be natural numbers and let $P^r:ℳ f_m → ℱℳ$ be the rth order frame bundle functor. Let $F:ℳ f_m → ℱℳ$ and $G:ℳ f_k → ℱℳ$ be natural bundles, where $k=dim (P^rℝ^m)$. We describe all $ℳ f_m$-natural operators A transforming sections σ of $FM → M$ and classical linear connections ∇ on M into sections A(σ,∇) of $G(P^rM) → P^rM$. We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.},
author = {J. Kurek, W. M. Mikulski},
journal = {Annales Polonici Mathematici},
keywords = {natural bundle; natural operator; classical connection},
language = {eng},
number = {1},
pages = {63-71},
title = {Lifting to the r-frame bundle by means of connections},
url = {http://eudml.org/doc/280755},
volume = {97},
year = {2010},
}

TY - JOUR
AU - J. Kurek
AU - W. M. Mikulski
TI - Lifting to the r-frame bundle by means of connections
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 1
SP - 63
EP - 71
AB - Let m and r be natural numbers and let $P^r:ℳ f_m → ℱℳ$ be the rth order frame bundle functor. Let $F:ℳ f_m → ℱℳ$ and $G:ℳ f_k → ℱℳ$ be natural bundles, where $k=dim (P^rℝ^m)$. We describe all $ℳ f_m$-natural operators A transforming sections σ of $FM → M$ and classical linear connections ∇ on M into sections A(σ,∇) of $G(P^rM) → P^rM$. We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.
LA - eng
KW - natural bundle; natural operator; classical connection
UR - http://eudml.org/doc/280755
ER -