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

Ku Yong Ha; Jong Bum Lee

首页> 外文期刊>Mathematische Nachrichten >Left invariant metrics and curvatures on simply connected three-dimensional Lie groups

【24h】

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

机译：简单连接的三维李群上的左不变度量和曲率

获取原文

获取原文并翻译 | 示例

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

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].

机译：对于每个简单连接的三维李群，我们确定了自同构组，将左不变黎曼度量分类为自同构，并研究了度量变化可以改变曲率的程度。由此，我们获得了三维李群上的主Ricci曲率，标量曲率和截面曲率作为左不变度量的函数。在三维情况下，我们的结果改善了Milnor [7]的结果，并改善了Kowalski和Nikvcevic的结果[6，定理3.1和4.1]。

著录项

来源
《Mathematische Nachrichten》 |2009年第6期|共31页
作者
Ku Yong Ha; Jong Bum Lee;
展开▼
作者单位

展开▼
收录信息
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Automorphism group; Curvature; Left invariant metric; Three-dimensional Lie groups;

机译：自同构群;曲率;左不变度量;三维李群;

相似文献

外文文献
中文文献
专利

1. Left invariant metrics and curvatures on simply connected three-dimensional Lie groups [J] . Ku Yong Ha, Jong Bum Lee Mathematische Nachrichten . 2009,第6期

机译：简单连接的三维李群上的左不变度量和曲率
2. LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS [J] . L. MAGNIN International journal of algebra and computation . 2007,第1期

机译：幂等势简单连通不可分解6维实李群的左不变结构
3. The signature of the Ricci curvature of left-invariant Riemannian metrics on nilpotent Lie groups [J] . Ngaha M. B. Djiadeu, Boucetta M., Kamga J. Wouafo Differential geometry and its applications . 2016,第Null期

机译：幂等李群上左不变黎曼度量的Ricci曲率的签名
4. Non-linear observer on Lie Groups for left-invariant dynamics with right-left equivariant output [C] . Silvere Bonnabel, Philippe Martin, Pierre Rouchon IFAC World Congress . 2008

机译：左侧左右动态的谎言组非线性观察者，具有右左上方的输出
5. Volume growth of left invariant sub-Riemannian geodesic balls in simply connected solvable Lie groups [D] . Bayrooti, Afshin 1997

机译：简单连接的可解李群中左不变黎曼次测球的体积增长
6. On the structure of complete simply-connected Kähler manifolds with nonpositive curvature [O] . Yum-Tong Siu, Shing-Tung Yau 1976

机译：关于具有正曲率的完全简单连通的Kähler流形的结构
7. On the δ-Pinching Function of the Sectional Curvature of a Compact Connected Lie Group G with a Bi-Invariant Riemannian Metric and a Vectorial Torsion Connection [O] . E.D. Rodionov, O.P. Khromova 2020

机译：关于紧凑型黎曼度量的紧凑型LIE组G截面曲率的δ夹紧函数及六边形扭转连接

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

摘要

著录项

相似文献

相关主题

期刊订阅