Milnor-type theorems for left-invariant Riemannian metrics on Lie groups
Milnor-type theorems for left-invariant Riemannian metrics on Lie groups
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DOI：
10.2969/jmsj/06820669
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Takahiro Hashinaga;H. Tamaru;Kazuhiro Terada
中科院分区：
文献类型：
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作者：
Takahiro Hashinaga;H. Tamaru;Kazuhiro Terada
对于三维幺模李群上的所有左不变黎曼度量，存在特殊的左不变标准正交框架，即所谓的Milnor框架。本文对李群上的任意左不变黎曼度量，给出了一个类似于Milnor框架的方法，使得它们之间的括号关系可以用相对较少的参数来表示.我们的程序是基于模空间的左不变黎曼度量。还将给出这种框架和应用的一些明确的例子。
For all left-invariant Riemannian metrics on three-dimensional unimodular Lie groups, there exist particular left-invariant orthonormal frames, so-called Milnor frames. In this paper, for any left-invariant Riemannian metrics on any Lie groups, we give a procedure to obtain an analogous of Milnor frames, in the sense that the bracket relations among them can be written with relatively smaller number of parameters. Our procedure is based on the moduli space of left-invariant Riemannian metrics. Some explicit examples of such frames and applications will also be given.