Submersions on open symplectic manifolds

Let M be an open manifold with a symplectic form Ω, and N a manifold with dim N < dim M . We prove that submersions f : ( M , Ω ) → N with symplectic fibres satisfy the h-principle. Such submersions define Dirac manifold structures on the given manifold. As an application to this result we show that C P n ∖ C P k − 1 admits a submersion into R 2 ( 2 k − n ) with symplectic fibres for n / 2 < k ⩽ n .