COMPLETE CLASSIFICATION OF PARALLEL SURFACES IN 4-DIMENSIONAL LORENTZIAN SPACE FORMS

被引：29

作者：

Chen, Bang-Yen ^{[1
]}

Van der Veken, Joeri ^{[2
]}

机构：

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

[2] Katholieke Univ Leuven, Dept Wiskunde, B-3001 Louvain, Belgium

来源：

TOHOKU MATHEMATICAL JOURNAL | 2009年 / 61卷 / 01期

基金：

比利时弗兰德研究基金会;

关键词：

Lorentzian space form; parallel second fundamental form; surface with parallel mean curvature vector; parallel surface; IMMERSIONS; SINGULARITIES; SUBMANIFOLDS;

D O I：

10.2748/tmj/1238764545

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we completely classify parallel non-degenerate surfaces in 4-dimensional Lorentzian space forms. In addition, we also completely classify non-degenerate surfaces with parallel mean curvature vector in 4-dimensional Lorentzian space forms.

引用

页码：1 / 40

页数：40

共 18 条

[1]

[Anonymous], SEMIRIEMANNIAN GEOME

[2]

[Anonymous], 1973, PURE APPL MATH

[3]

BLOMSTROM C, 1984, LECT NOTES MATH, V1156, P30

[4]

Chen B-Y., 1984, SER PURE MATH, V1

[5] Marginally trapped surfaces in Lorentzian space forms with positive relative nullity [J].

Chen, Bang-Yen ;

Van der Veken, Joeri .

CLASSICAL AND QUANTUM GRAVITY, 2007, 24 (03) :551-563

[6] Spatial and Lorentzian surfaces in Robertson-Walker space times [J].

Chen, Bang-Yen ;

Van der Veken, Joeri .

JOURNAL OF MATHEMATICAL PHYSICS, 2007, 48 (07)

[7]

CHEN BY, HOUSTON J M IN PRESS

[8]

Dajczer M., 1981, Manifolds and Lie Groups, P71

[9] IMMERSIONS WITH PARALLEL SECOND FUNDAMENTAL FORM [J].

FERUS, D .

MATHEMATISCHE ZEITSCHRIFT, 1974, 140 (01) :87-92

[10]

GRAVES L, 1979, TSUKUBA J MATH, V3, P17

← 1 2 →