On embeddings of almost complex manifolds in almost complex Euclidean spaces

摘要

We prove that any compact almost complex manifold (M-2m, J) of real dimension 2m admits a pseudo-holomorphic embedding in (R4m+2, (J) over tilde) for a suitable positive almost complex structure (J) over tilde. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class s(m) (M, J), for the existence of an embedding or an immersion in (R-4m, (J) over tilde). We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in (R-6, (J) over tilde). (C) 2015 Elsevier B.V. All rights reserved.