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The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --> M and ξ' --> M are equivalent if there exist smooth fibered-linear mapsξ --> ξ' and W: ξ --> 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) > 2. Under favorable conditions the same holds at points where the rank of ω changes from =2 to >2. Global versions are also considered.
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 --> M and ξ' --> M are equivalent if there exist smooth fibered-linear mapsξ --> ξ' and W: ξ --> 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) > 2. Under favorable conditions the same holds at points where the rank of ω changes from =2 to >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 --> M and ξ' --> M are equivalent if there exist smooth fibered-linear mapsξ --> ξ' and W: ξ --> 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) > 2. Under favorable conditions the same holds at points where the rank of ω changes from =2 to >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 -