On the characteristic direction of real hypersurfaces in and a symmetry result-Reference-Cited by-同舟云学术

On the characteristic direction of real hypersurfaces in and a symmetry result

Published:2010-04-12 Issue:3 Volume:10 Page:371-377
ISSN:1615-7168
Container-title:advg
language:en
Short-container-title:

Author:

Martino Vittorio¹,Montanari Annamaria¹

Affiliation:

1. Dipartimento di Matematica, Università di Bologna, piazza di Porta, S. Donato 5, 40127 Bologna, Italy. Email:

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom.2010.022/pdf

Reference7 articles.

1. A characteristic property of spheres

2. A sphere theorem for a class of Reinhardt domains with constant Levi curvature

3. Real hypersurfaces in Kähler manifolds

4. Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems

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