Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves

被引:19
作者
Castro, Ildefonso [1 ]
Chen, Bang-Yen
机构
[1] Univ Jaen, Escuela Politecn Super, Dept Matemat, Jaen 23071, Spain
[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
关键词
Legendre curve; Lagrangian immersion; Hamiltonian-minimal; elastica; minimal immersion; Lagrangian tori with constant mean curvature; Lagrangian angle map;
D O I
10.2748/tmj/1170347690
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane C-2 by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Will-more surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willinore surfaces in C-2.
引用
收藏
页码:565 / 579
页数:15
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