Every real ellipsoid in ℂ² admits CR umbilical points

Huang, Xiaojun; Ji, Shanyu

doi:10.1090/S0002-9947-06-04069-4

Every real ellipsoid in $\mathbb {C}^2$ admits CR umbilical points
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Trans. Amer. Math. Soc. 359 (2007), 1191-1204 Request permission

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 $n\ge 3$ does not admit any umbilical point.

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