# Levi umbilical surfaces in complex space

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

[BibTeX]

Accepted Paper

Inserted: 8 jul 2005
Last Updated: 26 jul 2006

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

Abstract:

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.