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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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CR regular embeddings of $S^{4n-1}$ in $\mathbb {C}^{2n+1}$
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by Naohiko Kasuya PDF
Proc. Amer. Math. Soc. 148 (2020), 3021-3024 Request permission

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
  • MR Author ID: 1037602
  • Email: nkasuya@cc.kyoto-su.ac.jp
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 3021-3024
  • MSC (2010): Primary 32V40, 53C40; Secondary 57R40
  • DOI: https://doi.org/10.1090/proc/14962
  • MathSciNet review: 4099788