The jet prolongations of $2$-fibred manifolds and the flow operator

Mikulski, Włodzimierz M.. "The jet prolongations of $2$-fibred manifolds and the flow operator." Archivum Mathematicum 044.1 (2008): 17-21. <http://eudml.org/doc/250287>.

@article{Mikulski2008,
abstract = {Let $r$, $s$, $m$, $n$, $q$ be natural numbers such that $s\ge r$. We prove that any $2$-$\{\mathcal \{F\}\}\mathbb \{M\}_\{m,n,q\}$-natural operator $A\colon T_\{\operatorname\{2-proj\}\}\rightsquigarrow TJ^\{(s,r)\}$ transforming $2$-projectable vector fields $V$ on $(m,n,q)$-dimensional $2$-fibred manifolds $Y\rightarrow X\rightarrow M$ into vector fields $A(V)$ on the $(s,r)$-jet prolongation bundle $J^\{(s,r)\}Y$ is a constant multiple of the flow operator $\mathcal \{J\}^\{(s,r)\}$.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {$(s,r)$-jet; bundle functor; natural operator; flow operator; $2$-fibred manifold; $2$-projectable vector field; -jet; bundle functor; natural operator; flow operator; 2-fibred manifold; 2-projectable vector field},
language = {eng},
number = {1},
pages = {17-21},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The jet prolongations of $2$-fibred manifolds and the flow operator},
url = {http://eudml.org/doc/250287},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - The jet prolongations of $2$-fibred manifolds and the flow operator
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 1
SP - 17
EP - 21
AB - Let $r$, $s$, $m$, $n$, $q$ be natural numbers such that $s\ge r$. We prove that any $2$-${\mathcal {F}}\mathbb {M}_{m,n,q}$-natural operator $A\colon T_{\operatorname{2-proj}}\rightsquigarrow TJ^{(s,r)}$ transforming $2$-projectable vector fields $V$ on $(m,n,q)$-dimensional $2$-fibred manifolds $Y\rightarrow X\rightarrow M$ into vector fields $A(V)$ on the $(s,r)$-jet prolongation bundle $J^{(s,r)}Y$ is a constant multiple of the flow operator $\mathcal {J}^{(s,r)}$.
LA - eng
KW - $(s,r)$-jet; bundle functor; natural operator; flow operator; $2$-fibred manifold; $2$-projectable vector field; -jet; bundle functor; natural operator; flow operator; 2-fibred manifold; 2-projectable vector field
UR - http://eudml.org/doc/250287
ER -