We apply Donaldson-Auroux's asymptotically holomorphic methods to construct asymptotically holomorphic embeddings of presymplectic closed manifolds of constant rank with integral form into Grassmannians . In particular, we obtain asymptotically holomorphic embeddings into the projective spaces such that the pull-back of the Fubini-Study form is cohomologous to for large integers . Moreover, we can construct asymptotically holomorphic immersions along the symplectic distribution of presymplectic manifolds into the projective spaces.
"Asymptotically holomorphic embeddings of presymplectic manifolds." J. Math. Soc. Japan 60 (3) 905 - 933, July, 2008. https://doi.org/10.2969/jmsj/06030905