JournalsrmiVol. 2, No. 4pp. 397–403

Forms Equivalent to Curvatures

  • Horacio Porta

    University of Illinois, Urbana, USA
  • Lázaro Recht

    Universidad Simón Bolívar, Caracas, Venezuela
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Abstract

The 2-forms, Ω\Omega and Ω\Omega ' on a manifold MM with values in vector bundles ξM\xi \rightarrow M and ξM\xi ' \rightarrow M are equivalentequivalent if there exist smooth fibered-linear maps U:ξξU: \xi \rightarrow \xi ' and W:ξξW: \xi ' \rightarrow \xi with Ω=UΩ\Omega ' = U\Omega and Ω=WΩ\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 (ω)=2(\omega) = 2 or in the set rank (ω)>2(\omega) > 2. Under favorable conditions the same holds at points where the rank of ω\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