A Bernstein-type theorem for Riemannian manifolds with a Killing field |
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Authors: | Luis J. Alías Marcos Dajczer Jaime Ripoll |
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Affiliation: | 1.Departamento de Matemáticas,Universidad de Murcia,Espinardo,Spain;2.IMPA,Rio de Janeiro,Brazil;3.Instituto de Matemática,Universidade Federal do Rio Grande do Sul,Porto Alegre,Brazil |
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Abstract: | The classical Bernstein theorem asserts that any complete minimal surface in Euclidean space that can be written as the graph of a function on must be a plane. In this paper, we extend Bernstein’s result to complete minimal surfaces in (may be non-complete) ambient spaces of non-negative Ricci curvature carrying a Killing field. This is done under the assumption that the sign of the angle function between a global Gauss map and the Killing field remains unchanged along the surface. In fact, our main result only requires the presence of a homothetic Killing field. L.J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02, F. Séneca project 00625/PI/04, and F. Séneca grant 01798/EE/05, Spain |
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Keywords: | Complete minimal surface Bernstein theorem Homothetic Killing field |
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