Martino, Vittorio ; Montanari, Annamaria
(2008)
On the Characteristic Direction of Real Hypersurfaces in C^(N+1) and a Symmetry Result.
[Preprint]
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Abstract
In this paper we show the following property of a non Levi flat real hypersurface in C^(n+1): if the unit characteristic direction T is a geodesic, then it is an eigenvector of the second fundamental form and the relative eigenvalue is constant. As an application we prove a symmetry result, of Alexandrov type, for compact hypersurfaces in C^(n+1) with positive constant Levi mean curvature.
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