On the obstruction to integrability of almost-complex structures

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158127The natural bundle $π:E\to M$ 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 pagesDifferential GeometryMathematical Physics53C15; 53A55; 53C10On the obstruction to integrability of almost-complex structurestext