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Every real ellipsoid in $ \mathbb{C}^2$ admits CR umbilical points

Author(s): Xiaojun Huang; Shanyu Ji
Journal: Trans. Amer. Math. Soc. 359 (2007), 1191-1204.
MSC (2000): Primary 32V40
Posted: August 15, 2006
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Abstract: We prove that every real ellipsoid $ M\subset\mathbb{C}^2$ admits at least four umbilical points, which can be compared to the result of Webster that a generic real ellipsoid in $ \mathbb{C}^n$ with $ n\ge3$ does not admit any umbilical point.

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Additional Information:

Xiaojun Huang
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: huangx@math.rutgers.edu

Shanyu Ji
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: shanyuji@math.uh.edu

DOI: 10.1090/S0002-9947-06-04069-4
PII: S 0002-9947(06)04069-4
Received by editor(s): December 9, 2004
Posted: August 15, 2006
Additional Notes: The first author was supported in part by NSF-0500626
Dedicated: To the memory of Professor S. S. Chern
Copyright of article: Copyright 2006, American Mathematical Society

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