An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space

  • Rafael Torres

    SISSA, Trieste, Italy
An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space cover
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Abstract

We show that a pseudo-holomorphic embedding of an almost-complex 2n2n-manifold into almost-complex (2n+2)(2n + 2)-Euclidean space exists if and only if there is a CR regular embedding of the 2n2n-manifold into complex (n+1)(n + 1)-space. We remark that the fundamental group does not place any restriction on the existence of either kind of embedding when nn 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 R8\mathbb R^8 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. 165–180

DOI 10.4171/LEM/63-1/2-5