Forms equivalent to curvatures.

Porta, Horacio, and Recht, Lázaro. "Forms equivalent to curvatures.." Revista Matemática Iberoamericana 2.4 (1986): 397-403. <http://eudml.org/doc/39336>.

@article{Porta1986,
abstract = {The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --&gt; M and ξ' --&gt; M are equivalent if there exist smooth fibered-linear mapsξ --&gt; ξ' and W: ξ --&gt; ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) &gt; 2. Under favorable conditions the same holds at points where the rank of ω changes from =2 to &gt;2. Global versions are also considered.},
author = {Porta, Horacio, Recht, Lázaro},
journal = {Revista Matemática Iberoamericana},
keywords = {Forma diferencial global; Curvatura; parallel transport; connection; 2-form; curvature; integrating factors},
language = {eng},
number = {4},
pages = {397-403},
title = {Forms equivalent to curvatures.},
url = {http://eudml.org/doc/39336},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Porta, Horacio
AU - Recht, Lázaro
TI - Forms equivalent to curvatures.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 4
SP - 397
EP - 403
AB - The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --&gt; M and ξ' --&gt; M are equivalent if there exist smooth fibered-linear mapsξ --&gt; ξ' and W: ξ --&gt; ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) &gt; 2. Under favorable conditions the same holds at points where the rank of ω changes from =2 to &gt;2. Global versions are also considered.
LA - eng
KW - Forma diferencial global; Curvatura; parallel transport; connection; 2-form; curvature; integrating factors
UR - http://eudml.org/doc/39336
ER -