I've started recently to learn about complex differential geometry and Kähler manifolds.
Let be $(M,J)$ a manifold with an almost complex structure embedded; I know that if we're able to define a closed (1,1) canonical form, then we can endow $(M,J)$ with a Kähler manifold structure.
Is it always possible to define a closed canonical form over any manifold like this? What are the necessary and sufficient conditions over the manifold or the inherent topological space?