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.
V. Martino, A.Montanari (2010). On the characteristic direction of real hypersurfaces in C^{n+1} and a symmetry result. ADVANCES IN GEOMETRY, 10, Issue 3, 371-377 [10.1515/ADVGEOM.2010.022].
On the characteristic direction of real hypersurfaces in C^{n+1} and a symmetry result
MARTINO, VITTORIO;MONTANARI, ANNAMARIA
2010
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.File in questo prodotto:
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