Timelike surfaces in the Lorentz-Minkowski space with prescribed Gaussian curvature and Gauss map

被引：9

作者：

Aledo, Juan A.

Espinar, José M.

Gálvez, José A. ^{[1
]}

机构：

[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

[2] Univ Castilla La Mancha, EPSA, Dept Matemat, E-02071 Albacete, Spain

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2006年 / 56卷 / 08期

关键词：

complete timelike surfaces; Kemnotsu-type representation; Gaussian curvature; harmonic maps;

D O I：

10.1016/j.geomphys.2005.07.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we obtain a Kenmotsu-type representation for timelike surfaces with prescribed Gauss map in the three-dimensional Lorentz-Minkowski space L-3. We use such representation in order to classify the complete timelike surfaces with positive constant Gaussian curvature in L3 in terms of harmonic diffeomorphisms between simply connected Lorentz surfaces and the universal covering of the de Sitter Space. (c) 2005 Elsevier B.V. All ri-hts reserved.

引用

页码：1357 / 1369

页数：13

共 50 条

[1] On the Gaussian curvature of timelike surfaces in Lorentz-Minkowski 3-space
Mazlum, Sumeyye Gur
[J]. FILOMAT, 2023, 37 (28) : 9641 - 9656
[2] Surfaces of constant Gauss curvature in Lorentz-Minkowski three-space
López, R
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2003, 33 (03) : 971 - 993
[3] Bjorling problem for timelike surfaces in the Lorentz-Minkowski space
Chaves, R. M. B.
Dussan, M. P.
Magid, M.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 377 (02) : 481 - 494
[4] On the curvatures of timelike circular surfaces in Lorentz-Minkowski space
Li, Jing
Yang, Zhichao
Li, Yanlin
Abdel-Baky, R. A.
Saad, M. Khalifa
[J]. FILOMAT, 2024, 38 (04) : 1423 - 1437
[5] On a prescribed mean curvature equation in Lorentz-Minkowski space
Azzollini, A.
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2016, 106 (06): : 1122 - 1140
[6] ON THE GAUSS CURVATURE OF MAXIMAL SURFACES IN THE 3-DIMENSIONAL LORENTZ-MINKOWSKI SPACE
ESTUDILLO, FJM
ROMERO, A
[J]. COMMENTARII MATHEMATICI HELVETICI, 1994, 69 (01) : 1 - 4
[7] Solutions of the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space
Kaya, Seher
Lopez, Rafael
[J]. TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (05) : 2186 - 2201
[8] Geometric properties of timelike surfaces in Lorentz-Minkowski 3-space
Mazlum, Sumeyye Gur
[J]. FILOMAT, 2023, 37 (17) : 5735 - 5749
[9] SPACELIKE RADIAL GRAPHS OF PRESCRIBED MEAN CURVATURE IN THE LORENTZ-MINKOWSKI SPACE
Bonheure, Denis
Iacopetti, Alessandro
[J]. ANALYSIS & PDE, 2019, 12 (07): : 1805 - 1842
[10] Immersed surfaces of prescribed Gauss curvature into Minkowski space
Ge, YX
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (07) : 2093 - 2101

← 1 2 3 4 5 →