CR regular embeddings of 𝑆⁴ⁿ⁻¹ in ℂ²ⁿ⁺¹

Kasuya, Naohiko

doi:10.1090/proc/14962

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