Maximal spacelike surfaces in a certain homogeneous Lorentzian 3-manifold

被引：0
|
作者：
Lee, Sungwook [1 ]
机构：
[1] Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USA
来源：
JOURNAL OF GEOMETRY | 2021年 / 112卷 / 02期
关键词：
Anti-de Sitter space; harmonic map; homogeneous manifold; Lorentzian manifold; maximal surface; Minkowski space; spacelike surface; solvable Lie group; MINIMAL-SURFACES; HARMONIC MAPS; REPRESENTATION;
D O I：
10.1007/s00022-021-00591-6
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 and anti-de Sitter 3-space, 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 for maximal spacelike surfaces in the homogeneous Lorentzian 3-manifolds is obtained. The normal Gauss map of maximal spacelike surfaces and its harmonicity are discussed.
引用
收藏
页数：13
相关论文
共 50 条
  • [31] NONORIENTABLE MAXIMAL SURFACES IN THE LORENTZ-MINKOWSKI 3-SPACE
    Fujimori, Shoichi
    Lopez, Francisco J.
    TOHOKU MATHEMATICAL JOURNAL, 2010, 62 (03) : 311 - 328
  • [32] ON THE TRANSVERSAL INTERSECTION CURVE OF SPACELIKE AND TIMELIKE SURFACES IN MINKOWSKI 3-SPACE
    Karaahmetoglu, Savas
    Aydemir, Ismail
    JOURNAL OF SCIENCE AND ARTS, 2016, (04) : 345 - 356
  • [33] Laguerre homogeneous surfaces in R3
    Li TongZhu
    SCIENCE CHINA-MATHEMATICS, 2012, 55 (06) : 1197 - 1214
  • [34] On lorentzian surfaces with H2 = K in Minkowski 3-space
    Ji, Fenghui
    Hou, Zhong Hua
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (01) : 54 - 58
  • [35] ON TRANSLATION SURFACES WITH ZERO GAUSSIAN CURVATURE IN LORENTZIAN SOL3 SPACE
    Belarbi, Lakehal
    Zoubir, Hanifi
    JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2022, 40 (5-6): : 831 - 842
  • [36] On the mean curvature of spacelike surfaces in certain three-dimensional Robertson–Walker spacetimes and Calabi–Bernstein’s type problems
    Alfonso Romero
    Rafael M. Rubio
    Annals of Global Analysis and Geometry, 2010, 37 : 21 - 31
  • [37] HIGHER GENUS NONORIENTABLE MAXIMAL SURFACES IN THE LORENTZ-MINKOWSKI 3-SPACE
    Fujimori, Shoichi
    Kaneda, Shin
    TOHOKU MATHEMATICAL JOURNAL, 2023, 75 (01) : 1 - 14
  • [38] Totally umbilic surfaces in homogeneous 3-manifolds
    Souam, Rabah
    Toubiana, Eric
    COMMENTARII MATHEMATICI HELVETICI, 2009, 84 (03) : 673 - 704
  • [39] Sweeping surfaces generated by involutes of a spacelike curve with a timelike binormal in Minkowski 3-space
    Kalkan, Ozgur Boyacioglu
    Senyurt, Suleyman
    Bilici, Mustafa
    Canli, Davut
    AIMS MATHEMATICS, 2025, 10 (01): : 988 - 1007
  • [40] Representation of Maximal Surfaces in a 3-Dimensional Lightlike Cone
    Qian, Jinhua
    Fu, Xueshan
    Liu, Huili
    MATHEMATICS, 2020, 8 (11) : 1 - 11
12345