On the obstruction to integrability of almost-complex structures
Abstract
The natural bundle π:E M of almost-complex structures is considered. The action of the pseudogroup of all diffeomorphisms of M on the total space E is investigated. A nontrivial 1-st order differential invariant of this action is constructed. It is proved that the Nijenhuise tensor of an almost-complex structures is equal to zero iff the constructed invariant for this structure is zero.
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