Porta, Horacio; Recht, Lázaro Forms equivalent to curvatures. (English) Zbl 0632.53031 Rev. Mat. Iberoam. 2, No. 3-4, 397-403 (1986). Two 2-forms \(\Omega\) and \(\Omega\) ’ on a manifold M with values in vector bundles \(\xi\to M\) and \(\xi\) ’\(\to M\) are said to be equivalent, if there exist smooth fibered-linear maps \(U: \xi\to \xi '\) and \(W: \xi\) ’\(\to \xi\) such that \(\Omega '=U\Omega\) and \(\Omega =W\Omega '\). Near a point \(x\in M\), a 2-form \(\omega\) is said to have an integrating factor f, if \(f\omega\) is closed near x. Let \(\theta\to M\) be a bundle endowed with a connection. Now a theorem, for example, states that: a 2-form \(\omega\) equivalent to the curvature has an integrating factor near x, if \(rank(\omega)=2\) near x or \(rank(\omega)>2\) near x. Some other theorems and propositions are stated, which are also related to the local or global integrating factors. Reviewer: H.Wakakuwa MSC: 53C05 Connections (general theory) 58A10 Differential forms in global analysis Keywords:parallel transport; connection; 2-form; curvature; integrating factors PDFBibTeX XMLCite \textit{H. Porta} and \textit{L. Recht}, Rev. Mat. Iberoam. 2, No. 3--4, 397--403 (1986; Zbl 0632.53031) Full Text: DOI EuDML