On embeddings of almost complex manifolds in almost complex Euclidean spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:101

Article

Di Scala, Antonio J.¹  Kasuya, Naohiko²  Zuddas, Daniele³ 

[1] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Aoyama Gakuin Univ, Dept Social Informat, Chuo Ku, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 2525258, Japan

[3] Korea Inst Adv Study, 85 Hoegiro, Seoul 02455, South Korea

关键词: Almost complex manifold;    Pseudo-holomorphic embedding;    Immersion;   

DOI  :  10.1016/j.geomphys.2015.11.008

来源: Elsevier

【 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.

【 授权许可】

Free