A Bernstein-type theorem for Riemannian manifolds with a Killing field

被引:44
作者
Alias, Luis J.
Dajczer, Marcos
Ripoll, Jaime
机构
[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
[2] IMPA, BR-22460320 Rio De Janeiro, Brazil
[3] Univ Fed Rio Grande do Sul, Inst Matemat, BR-91501970 Porto Alegre, RS, Brazil
关键词
complete minimal surface; Bernstein theorem; homothetic Killing field;
D O I
10.1007/s10455-006-9045-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The classical Bernstein theorem asserts that any complete minimal surface in Euclidean space R-2 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.
引用
收藏
页码:363 / 373
页数:11
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