Levi umbilical surfaces in complex space

Details Levi umbilical surfaces in complex space Levi umbilical surfaces in complex space

2005-12-14

arxiv.org/abs/math/0512330v1

J. reine angew. Math. 603 (2007) 113-131

Mathematics

Differential Geometry

18 pages

Scientific paper

10.1515/CRELLE.2007.013

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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