Asymptotically holomorphic embeddings of presymplectic manifolds

Abstract

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 Gr(r,N). In particular, we obtain asymptotically holomorphic embeddings into the projective spaces CP^N-1 such that the pull-back of the Fubini-Study form is cohomologous to kω/2π for large integers k. Moreover, we can construct asymptotically holomorphic immersions along the symplectic distribution of presymplectic manifolds into the projective spaces.