# Forms Equivalent to Curvatures

### Horacio Porta

University of Illinois, Urbana, USA### Lázaro Recht

Universidad Simón Bolívar, Caracas, Venezuela

## Abstract

The 2-forms, $\Omega$ and $\Omega '$ on a manifold $M$ with values in vector bundles $\xi \rightarrow M$ and $\xi ' \rightarrow M$ are $equivalent$ if there exist smooth fibered-linear maps $U: \xi \rightarrow \xi '$ and $W: \xi ' \rightarrow \xi$ with $\Omega ' = U\Omega$ and $\Omega = W\Omega '$. 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 $(\omega) = 2$ or in the set rank $(\omega) > 2$. Under favorable conditions the same holds at points where the rank of $\omega$ 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. 397–403

DOI 10.4171/RMI/41