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CR regular embeddings of $ S^{4n-1}$ in $ \mathbb{C}^{2n+1}$


Author: Naohiko Kasuya
Journal: Proc. Amer. Math. Soc. 148 (2020), 3021-3024
MSC (2010): Primary 32V40, 53C40; Secondary 57R40
DOI: https://doi.org/10.1090/proc/14962
Published electronically: March 17, 2020
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Abstract: Ahern and Rudin have given an explicit construction of a totally real embedding of $ S^3$ in $ \mathbb{C}^3$. As a generalization of their example, we give an explicit example of a CR regular embedding of $ S^{4n-1}$ in $ \mathbb{C}^{2n+1}$. Consequently, we show that the odd dimensional sphere $ S^{2m-1}$ with $ m>1$ admits a CR regular embedding in $ \mathbb{C}^{m+1}$ if and only if $ m$ is even.


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Additional Information

Naohiko Kasuya
Affiliation: Department of Mathematics, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku, Kyoto, 603-8555, Japan
Email: nkasuya@cc.kyoto-su.ac.jp

DOI: https://doi.org/10.1090/proc/14962
Keywords: CR regular, totally real, embedding
Received by editor(s): September 26, 2019
Received by editor(s) in revised form: December 3, 2019
Published electronically: March 17, 2020
Additional Notes: The author was supported in part by the Grant-in-Aid for Young Scientists (B), No. 17K14193, Japan Society for the Promotion of Science
Communicated by: Harold P. Boas
Article copyright: © Copyright 2020 American Mathematical Society