Calculus of Variations and Geometric Measure Theory
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R. Monti - D. Morbidelli

Levi umbilical surfaces in complex space

created by monti on 08 Jul 2005
modified on 26 Jul 2006


Accepted Paper

Inserted: 8 jul 2005
Last Updated: 26 jul 2006

Journal: Journal fuer die Reine und Angewandte Mathematik
Year: 2006


We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such surfaces are contained either in a sphere or in the boundary of a complex tube domain with spherical section.


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