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On the characteristic direction of real hypersurfaces in and a symmetry result
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Vittorio Martino
Published/Copyright:
April 12, 2010
Abstract
In this paper we show the following property of a non Levi flat real hypersurface in 
: 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 with positive constant Levi mean curvature.
Received: 2007-11-10
Revised: 2009-02-12
Published Online: 2010-04-12
Published in Print: 2010-July
© de Gruyter 2010
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Articles in the same Issue
- On the characteristic direction of real hypersurfaces in and a symmetry result
- Small maximal partial spreads in classical finite polar spaces
- On antipodes on a convex polyhedron II
- On the quadratic normality and the triple curve of three-dimensional subvarieties of
- A generalization of the Giulietti–Korchmáros maximal curve
- Busemann Functions and the Julia–Wolff–Carathéodory Theorem for polydiscs
- Generalized polygons with non-discrete valuation defined by two-dimensional affine ℝ-buildings
- Measures on the space of convex bodies
- On the scalar curvature of hypersurfaces in spaces with a Killing field
- The real quadrangle of type E6
- Triple-point defective surfaces
- On surfaces with pg = 2q – 3
- A counter example to an ideal membership test
