A Function obstruction to the Existence of Complex Structures

Abstract

We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence of complex structures from the almost-complex structure. It is a function, not a tensor, so it is easier to work with.

6 pages. removed word "Riemannian" in introduction and general description, for emphasizing that result is independent of any Riemannian metric $g$ on the manifold