MINIMAL TIMELIKE SURFACES IN A CERTAIN HOMOGENEOUS LORENTZIAN 3-MANIFOLD

被引：0

作者：

Lee, Sungwook ^{[1
]}

机构：

[1] Univ Southern Mississippi, Dept Math, 118 Coll Dr,5045, Hattiesburg, MS 39406 USA

来源：

TOHOKU MATHEMATICAL JOURNAL | 2017年 / 69卷 / 04期

关键词：

De Sitter space; harmonic map; homogeneous manifold; Lorentz surface; Lorentzian manifold; Minkowski space; minimal surface; solvable Lie group; spacetime; timelike surface;

D O I：

10.2748/tmj/1512183633

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula which is the unification of representation formulas for minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds is obtained. The normal Gauss map of minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds and its harmonicity are discussed.

引用

页码：621 / 635

页数：15

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