Totally real embeddings of $S^ 3$ in $\textbf {C}^ 3$
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- by Patrick Ahern and Walter Rudin
- Proc. Amer. Math. Soc. 94 (1985), 460-462
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787894-7
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Abstract:
An explicit totally real embedding of ${S^3}$ in ${{\text {C}}^3}$ is exhibited. It has the form $F(z,w) = (z,w,P(z,w))$ where $P$ is a (nonholomorphic) polynomial of degree 4, and $(z,w)$ ranges over the unit sphere in ${{\text {C}}^2}$.References
- M. L. Gromov, Convex integration of differential relations. I, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 329β343 (Russian). MR 0413206
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594, DOI 10.1007/978-1-4613-8098-6
- Edgar Lee Stout and William R. Zame, Totally real imbeddings and the universal convering spaces of domains of holomorphy: some examples, Manuscripta Math. 50 (1985), 29β48. MR 784138, DOI 10.1007/BF01168826
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 460-462
- MSC: Primary 32F25; Secondary 57R40
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787894-7
- MathSciNet review: 787894