Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
Differential Geometry
2015-01-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1501.05513,
title = {Three-dimensional solvsolitons and the minimality of the corresponding submanifolds},
author = {Takahiro Hashinaga and Hiroshi Tamaru},
journal= {arXiv preprint arXiv:1501.05513},
year = {2015}
}
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29 pages