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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. Gromov, Convex integration of differential relations, Math. USSR-Izv. 7 (1973), 329-343. MR 0413206 (54:1323)
  • [2] W. Rudin, Function theory in the unit ball of $ {{\text{C}}^n}$, Springer-Verlag, Berlin and New York, 1980. MR 601594 (82i:32002)
  • [3] E. L. Stout and W. R. Zame, Totally real embeddings and the universal covering spaces of domains of holomorphy: some examples, Manuscripta Math. (to appear). MR 784138 (86h:32026)

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