Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
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三维解孤子和相应子流形的极小值
DOI：
10.1142/s0129167x17500483
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Hiroshi Tamaru
中科院分区：
文献类型：
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作者：
Takahiro Hashinaga;Hiroshi Tamaru
在本文中，我们定义了李群上左不变黎曼度量对应的子流形，并研究了以下问题：李群上的一个杰出的左不变黎曼度量是否对应于一个杰出的子流形？结果，我们证明了三维单连通可解李群上的解孤子完全由相应子流形的极小性来表征。
In this paper, we define the corresponding submanifolds to left-invariant Riemannian metrics on Lie groups, and study the following question: does a distinguished left-invariant Riemannian metric on a Lie group correspond to a distinguished submanifold? As a result, we prove that the solvsolitons on three-dimensional simply-connected solvable Lie groups are completely characterized by the minimality of the corresponding submanifolds.