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.
2017
63
1/2
165
180
http://www.ems-ph.org/journals/show_abstract.php?issn=0013-8584&vol=63&iss=1&rank=5
https://arxiv.org/abs/1804.07945
Torres Ruiz, Rafael
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/71593
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