Proceedings of the American Mathematical Society

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

 

 

Totally real embeddings of $ S\sp 3$ in $ {\bf C}\sp 3$


Authors: Patrick Ahern and Walter Rudin
Journal: Proc. Amer. Math. Soc. 94 (1985), 460-462
MSC: Primary 32F25; Secondary 57R40
MathSciNet review: 787894
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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 [Enhancements On Off] (What's this?)

  • [1] M. L. Gromov, Convex integration of differential relations. I, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 329–343 (Russian). MR 0413206
  • [2] Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
  • [3] 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), 29–48. MR 784138, 10.1007/BF01168826

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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787894-7
Article copyright: © Copyright 1985 American Mathematical Society