An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space
Rafael TorresSISSA, Trieste, Italy
We show that a pseudo-holomorphic embedding of an almost-complex -manifold into almost-complex -Euclidean space exists if and only if there is a CR regular embedding of the -manifold into complex -space. We remark that the fundamental group does not place any restriction on the existence of either kind of embedding when is at least three. We give necessary and sufficient conditions in terms of characteristic classes for a closed almost-complex 6-manifold to admit a pseudo-holomorphic embedding into equipped with an almost-complex structure that need not be integrable.
Cite this article
Rafael Torres, An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space. Enseign. Math. 63 (2017), no. 1/2, pp. 165–180DOI 10.4171/LEM/63-1/2-5