On the obstruction to integrability of almost-complex structures

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 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.

11 pages

References in corpus (2)

• Differential invariants of 2--order ODEs, I
• On the obstruction to linearizability of 2-order ordinary differential equations