**Definition** (** Open Manifolds**):An open manifold is a manifold without boundary with no compact component. For a connected manifold, "open" is equivalent to "without boundary and non-compact.
we know that every symplectic manifold admits an almost complex structure but for open manifolds , the inverse is also correct and infact ;

M.Gromov proved Every **open** almost complex manifold admits a symplectic
structure,

**So My question is** , how can we extend it for **Generalized Almost Complex manifolds**(in the sense of Hitchin and Gualtieri )?

Every **generalized open almost complex manifold** admits a **non trivial generalized symplectic
structure**?