We show that a pseudo-holomorphic embedding of an almost-complex 2n-manifold into almost-complex (2n+2)-Euclidean space exists if and only if there is a CR regular embedding of the 2n-manifold into complex (n+1)-space. We remark that the fundamental group does not place any restriction on the existence of either kind of embedding when n 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 equipped with an almost-complex structure that need not be integrable.
An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space / Torres Ruiz, Rafael. - In: L'ENSEIGNEMENT MATHÉMATIQUE. - ISSN 0013-8584. - 63:1/2(2017), pp. 165-180. [10.4171/LEM/63-1/2-5]
An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space
Rafael Torres
2017-01-01
Abstract
We show that a pseudo-holomorphic embedding of an almost-complex 2n-manifold into almost-complex (2n+2)-Euclidean space exists if and only if there is a CR regular embedding of the 2n-manifold into complex (n+1)-space. We remark that the fundamental group does not place any restriction on the existence of either kind of embedding when n 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 equipped with an almost-complex structure that need not be integrable.File | Dimensione | Formato | |
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