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On the minimality of the corresponding submanifolds to four-dimensional solvsolitons 4次元可解ソリトンに対応する部分多様体の極小性について 橋永, 貴弘 Hashinaga, Takahiro Lie groups left-invariant Riemannian metrics solvsolitons symmetric spaces minimal submanifolds 410 In our previous study, the author and Tamaru proved that a left invariant Riemannian metric on a three-dimensional simply-connected solvable Lie group is a solvsoliton if and only if the corresponding sub manifold is minimal. In this paper, we study the minimality of the corresponding sub manifolds to solvsolitons on four-dimensional cases. In four-dimensional nilpotent cases, we prove that a left-invariant Riemannian metric is a nilsoliton if and only if the corresponding sub manifold is minimal. On the other hand, there exists a four-dimensional simply-connected solvable Lie group so that the above correspondence does not hold. More precisely, there exists a solvsoliton whose corresponding sub manifold is not minimal, and a left-invariant Riemannian metric which is not solvsoliton and whose corresponding sub manifold is minimal. 博士(理学) Science http://purl.org/coar/resource_type/c_db06 広島大学 Hiroshima University 2014-03-23 NA 甲第6358号 https://hiroshima.repo.nii.ac.jp/records/2005160 eng Takahiro Hashinaga, On the minimality of the corresponding submanifolds to fourdimensional solvsolitons. Hiroshima Mathematical Journal (掲載決定) open access Copyright(c) by Author