On the obstruction to integrability of almost-complex structures

Details On the obstruction to integrability of almost-complex structures On the obstruction to integrability of almost-complex structures

2008-04-04

arxiv.org/abs/0804.0690v1

Mathematics

Differential Geometry

11 pages

Scientific paper

The natural bundle $\pi:E\to M$ 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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