We define a complex connection on a real hypersurface of Cnþ1 which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in Cnþ1, nf2, 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.
Levi umbilical surfaces in complex space
MONTI, ROBERTO;
2007
Abstract
We define a complex connection on a real hypersurface of Cnþ1 which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in Cnþ1, nf2, 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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