# On the obstruction to integrability of almost-complex structures - Mathematics > Differential Geometry

Abstract: 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 thisaction is constructed. It is proved that the Nijenhuise tensor of analmost-complex structures is equal to zero iff the constructed invariant forthis structure is zero.

Author: Valeriy A. Yumaguzhin

Source: https://arxiv.org/