The 2-forms, and on a manifold with values in vector bundles and are if there exist smooth fibered-linear maps and with and . 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 or in the set rank . Under favorable conditions the same holds at points where the rank of changes from =2 to >2. Global versions are also considered.
Cite this article
Horacio Porta, Lázaro Recht, Forms Equivalent to Curvatures. Rev. Mat. Iberoam. 2 (1986), no. 4, pp. 397–403DOI 10.4171/RMI/41