Surfaces in three-dimensional Lie groups

被引：25

作者：

Berdinsky, DA ^{[1
]}

Taimanov, IA

机构：

[1] Novosibirsk State Univ, Novosibirsk 630090, Russia

[2] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2005年 / 46卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

surface; three-dimensional Lie group; Weierstrass representation; Willmore functional;

D O I：

10.1007/s11202-005-0096-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive the Weierstrass (or spinor) representation for surfaces in the three-dimensional Lie groups Nil, (SL) over tilde (2), and Sol with Thurston's geometries and establish the generating equations for minimal surfaces in these groups. Using the spectral properties of the corresponding Dirac operators, we find analogs of the Willmore functional for surfaces in these geometries.

引用

页码：1005 / 1019

页数：15

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