- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:42
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
2
1986
4
Forms Equivalent to Curvatures
Horacio
Porta
University of Illinois, URBANA, UNITED STATES
Lázaro
Recht
Universidad Simón Bolívar, CARACAS, VENEZUELA
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.
General
397
403
10.4171/RMI/41
http://www.ems-ph.org/doi/10.4171/RMI/41