Electronic Resource
Springer
Manuscripta mathematica
55 (1986), S. 1-7
ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetV be a complex hypersurface in an open subset of ℂ3, and letM be a smooth compact real hypersurface inV. Using a theorem of Gromov we prove that there exist small C1 perturbations $$\tilde M$$ ofM in ℂ3 such that $$\tilde M$$ is a totally real submanifold of ℂ3. As a consequence we show that certain quotients of the three-sphere admit totally real embeddings into ℂ3. In some special cases including the real projective three-space we find explicit totally real embeddings into ℂ3. Our construction is similar to that of Ahern and Rudin who found a totally real embedding of the three-sphere into ℂ3.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01168610
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