On Lorentz dynamics: From group actions to warped products via homogeneous spaces

被引：6

作者：

Arouche, A.

Deffaf, M.

Zeghib, A.

机构：

[1] Univ Sci & Technol Houari Boumediene, Fac Math, Algiers, Algeria

[2] Ecole Normale Super Lyon, CNRS, UMPA, F-69364 Lyon, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 359卷 / 03期

关键词：

Lorentz manifolds; warped product; semi-simple transformation groups;

D O I：

10.1090/S0002-9947-06-04279-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show a geometric rigidity of isometric actions of non-compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.

引用

页码：1253 / 1263

页数：11

共 14 条

[1] The isometry group of a compact Lorentz manifold .1. [J].

Adams, S ;

Stuck, G .

INVENTIONES MATHEMATICAE, 1997, 129 (02) :239-261

[2] Dynamics of simple Lie groups on Lorentz manifolds [J].

Adams, S .

GEOMETRIAE DEDICATA, 2004, 105 (01) :1-12

[3]

Adams S, 1997, INVENT MATH, V129, P263, DOI 10.1007/s002220050164

[4]

[Anonymous], TRAVAUX COURS

[5] Isometric actions of Lie subgroups of the Moebius group [J].

Boubel, C ;

Zeghib, A .

NONLINEARITY, 2004, 17 (05) :1677-1688

[6] INTERNAL CHARACTERIZATION OF DISTORTED PRODUCTS [J].

HIEPKO, S .

MATHEMATISCHE ANNALEN, 1979, 241 (03) :209-215

[7]

KOWALSKY N, 1995, CR ACAD SCI I-MATH, V321, P595

[8]

KOWALSKY N, 1997, ANN MATH, V144, P611

[9] TWISTED PRODUCTS IN PSEUDO-RIEMANNIAN GEOMETRY [J].

PONGE, R ;

RECKZIEGEL, H .

GEOMETRIAE DEDICATA, 1993, 48 (01) :15-25

[10]

Witte D., 2001, BEITRAGE ALGEBRA GEO, V42, P451

← 1 2 →