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?

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 generalized symplectic structure?

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?

Every generalized open almost complex manifold admits a generalized symplectic structure?

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?

Every generalized open almost complex manifold admits a generalized symplectic structure?