CLASSIFICATION THEOREMS FOR SPACE-LIKE SURFACES IN 4-DIMENSIONAL INDEFINITE SPACE FORMS WITH INDEX 2

被引：2

作者：

Chen, Bang-Yen ^{[1
]}

Suceava, Bogdan D. ^{[2
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Calif State Univ Fullerton, Dept Math, Fullerton, CA 92854 USA

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2011年 / 15卷 / 02期

关键词：

Gauss curvature; Normal curvature; Wintgen ideal surface; Space-like surface; DESZCZ SYMMETRIES;

D O I：

10.11650/twjm/1500406219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Surfaces in 4D Riemannian space forms have been investigated extensively. In contrast, only few results are known for surfaces in 4D neutral indefinite space forms R-2(4)(c). Thus, in this paper we study space-like surfaces in R-2(4)(c) satisfying certain simple geometric properties. In particular, we classify space-like surfaces in E-2(4) with constant mean and Gauss curvatures and null normal curvature. We also classify Wintgen ideal surfaces in R-2(4)(c) whose Gauss and normal curvatures satisfy K-D = 2K.

引用

页码：523 / 541

页数：19

共 50 条

[31] Curvature estimate of steepest descents of 2-dimensional maximal space-like hypersurfaces on space forms
Peihe Wang
Jianchun Wang
Frontiers of Mathematics in China, 2020, 15 : 167 - 181
[32] Bernstein-type theorems for space-like surfaces with parallel mean curvature
Xin, YL
Ye, RG
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1997, 489 : 189 - 198
[33] EXTREME 2-DIMENSIONAL SURFACES IN 4-DIMENSIONAL EUCLIDEAN-SPACE
BERNIK, VI
KOVALEVSKAYA, EI
ACTA ARITHMETICA, 1990, 53 (04) : 333 - 349
[34] On biconservative hypersurfaces in 4-dimensional Riemannian space forms
Turgay, Nurettin Cenk
Upadhyay, Abhitosh
MATHEMATISCHE NACHRICHTEN, 2019, 292 (04) : 905 - 921
[35] Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space
Ou, Li
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2025, 99
[36] The convexity of the level sets of maximal strictly space-like hypersurfaces defined on 2-dimensional space forms
Wang, Peihe
Liu, Xiao
Liu, Zhonghua
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 174 : 79 - 103
[37] Space-like hypersurfaces with vanishing conformal forms in the conformal space
Huizhang, Yang
Xia, Sun
NOTE DI MATEMATICA, 2012, 32 (02): : 63 - 71
[38] Problem of functional extension and space-like surfaces in Minkowski space
Grigoryeva, EG
Klyachin, AA
Miklyukov, VM
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2002, 21 (03): : 719 - 752
[39] General rotational surfaces in the 4-dimensional Minkowski space
Ganchev, Georgi
Milousheva, Velichka
TURKISH JOURNAL OF MATHEMATICS, 2014, 38 (05) : 883 - 895
[40] SOME REPRESENTATION THEOREMS IN A 4-DIMENSIONAL INNER PRODUCT SPACE
PENNISI, S
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1986, 5 : 191 - 214

← 1 2 3 4 5 →