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Given a k-form f and an l-form g with 0 ≤ l ≤ k, we give necessary and sufficient conditions for the existence of a (k − l)-form u verifying
We have benefitted from interesting discussions with D. Serre and M. Troyanov. The research of the second author has been, in part, subsidized by a grant of the Fonds National Suisse de la Recherche Scientifique.
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