The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds

J. Kurek, and W. M. Mikulski. "The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds." Colloquium Mathematicae 97.2 (2003): 141-149. <http://eudml.org/doc/285048>.

@article{J2003,
abstract = {Let F:ℱ ℳ → ℬ be a vector bundle functor. First we classify all natural operators $T_\{proj|ℱ ℳ _\{m,n\}\} ⇝ T^\{(0,0)\}(F_\{|ℱ ℳ_\{m,n\}\})*$ transforming projectable vector fields on Y to functions on the dual bundle (FY)* for any $ℱ ℳ _\{m,n\}$-object Y. Next, under some assumption on F we study natural operators $T*_\{hor|ℱ ℳ _\{m,n\}\} ⇝ T*(F_\{|ℱ ℳ _\{m,n\}\})*$ lifting horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators $T*_\{hor|ℱ ℳ _\{m,n\}\} ⇝ T*(F_\{|ℱ ℳ _\{m,n\}\})*$ for some vector bundle functors F on fibered manifolds.},
author = {J. Kurek, W. M. Mikulski},
journal = {Colloquium Mathematicae},
keywords = {bundle functor; natural operator},
language = {eng},
number = {2},
pages = {141-149},
title = {The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds},
url = {http://eudml.org/doc/285048},
volume = {97},
year = {2003},
}

TY - JOUR
AU - J. Kurek
AU - W. M. Mikulski
TI - The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 2
SP - 141
EP - 149
AB - Let F:ℱ ℳ → ℬ be a vector bundle functor. First we classify all natural operators $T_{proj|ℱ ℳ _{m,n}} ⇝ T^{(0,0)}(F_{|ℱ ℳ_{m,n}})*$ transforming projectable vector fields on Y to functions on the dual bundle (FY)* for any $ℱ ℳ _{m,n}$-object Y. Next, under some assumption on F we study natural operators $T*_{hor|ℱ ℳ _{m,n}} ⇝ T*(F_{|ℱ ℳ _{m,n}})*$ lifting horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators $T*_{hor|ℱ ℳ _{m,n}} ⇝ T*(F_{|ℱ ℳ _{m,n}})*$ for some vector bundle functors F on fibered manifolds.
LA - eng
KW - bundle functor; natural operator
UR - http://eudml.org/doc/285048
ER -