Flow prolongation of some tangent valued forms

Cabras, Antonella, and Kolář, Ivan. "Flow prolongation of some tangent valued forms." Czechoslovak Mathematical Journal 58.2 (2008): 493-504. <http://eudml.org/doc/31225>.

@article{Cabras2008,
abstract = {We study the prolongation of semibasic projectable tangent valued $k$-forms on fibered manifolds with respect to a bundle functor $F$ on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear $r$-th order connection on the base manifold, where $r$ is the base order of $F$. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued $k$-forms in the case $F$ is a fiber product preserving bundle functor on the category of fibered manifolds with $m$-dimensional bases and local diffeomorphisms as base maps.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Czechoslovak Mathematical Journal},
keywords = {semibasic tangent valued $k$-form; Frölicher-Nijenhuis bracket; bundle functor; flow prolongation of vector fields; connection; curvature; semibasic tangent valued -form; Frölicher-Nijenhuis bracket; bundle functor; flow prolongation of vector fields; connection; curvature},
language = {eng},
number = {2},
pages = {493-504},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Flow prolongation of some tangent valued forms},
url = {http://eudml.org/doc/31225},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Flow prolongation of some tangent valued forms
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 493
EP - 504
AB - We study the prolongation of semibasic projectable tangent valued $k$-forms on fibered manifolds with respect to a bundle functor $F$ on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear $r$-th order connection on the base manifold, where $r$ is the base order of $F$. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued $k$-forms in the case $F$ is a fiber product preserving bundle functor on the category of fibered manifolds with $m$-dimensional bases and local diffeomorphisms as base maps.
LA - eng
KW - semibasic tangent valued $k$-form; Frölicher-Nijenhuis bracket; bundle functor; flow prolongation of vector fields; connection; curvature; semibasic tangent valued -form; Frölicher-Nijenhuis bracket; bundle functor; flow prolongation of vector fields; connection; curvature
UR - http://eudml.org/doc/31225
ER -