Resumen de Forms Equivalent to Curvature.

Horacio Porta, Lázaro Recht

• The 2-forms, O and O' on a manifold M with values in vector bundles ? --> M and ?' --> M are equivalent if there exist smooth fibered-linear maps ? --> ?' and W: ? --> ?' with O' = UO and O = WO'. 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 (?) = 2 or in the set rank (?) > 2. Under favorable conditions the same holds at points where the rank of ? changes from =2 to >2. Global versions are also considered.