Left invariant metrics and curvatures on simply connected three-dimensional Lie groups

被引：58

作者：

Ha, Ku Yong ^{[2
]}

Lee, Jong Bum ^{[1
]}

机构：

[1] Sogang Univ, Dept Math, Seoul 121742, South Korea

[2] Seoul Natl Univ, Res Inst Basic Sci, Seoul 151747, South Korea

来源：

MATHEMATISCHE NACHRICHTEN | 2009年 / 282卷 / 06期

关键词：

Automorphism group; curvature; left invariant metric; three-dimensional Lie groups;

D O I：

10.1002/mana.200610777

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For each simply connected three-dimensional Lie group we determine the automorphism group, classify the left invariant Riemannian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the principal Ricci curvatures, the scalar curvature and the sectional curvatures as functions of left invariant metrics on the three-dimensional Lie groups. Our results improve a bit of Milnor's results of [7] in the three-dimensional case, and Kowalski and Nikvcevic's results [6, Theorems 3.1 and 4. 1]. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：868 / 898

页数：31

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