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Levi umbilical surfaces in complex space

R. Monti·D. Morbidelli
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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.

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R. Monti, D. Morbidelli. 2005-12-14. Levi umbilical surfaces in complex space. https://doi.org/10.1515/crelle.2007.013

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