Levi umbilical surfaces in complex space

none2Abstract. 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 geq 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.noneR. Monti; D. MorbidelliR. Monti; D. Morbidell