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July 2014 On the minimality of the corresponding submanifolds to four-dimensional solvsolitons
Takahiro Hashinaga
Hiroshima Math. J. 44(2): 173-191 (July 2014). DOI: 10.32917/hmj/1408972906

Abstract

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 submanifold is minimal. In this paper, we study the minimality of the corresponding submanifolds to solvsolitons on fourdimensional cases. In four-dimensional nilpotent cases, we prove that a left-invariant Riemannian metric is a nilsoliton if and only if the corresponding submanifold is minimal. On the other hand, there exists a four-dimensional simply-connected solvable Lie group so that the above correspondence dose not hold. More precisely, there exists a solvsoliton whose corresponding submanifold is not minimal, and a left-invariant Riemannian metric which is not solvsoliton and whose corresponding submanifold is minimal.

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Takahiro Hashinaga. "On the minimality of the corresponding submanifolds to four-dimensional solvsolitons." Hiroshima Math. J. 44 (2) 173 - 191, July 2014. https://doi.org/10.32917/hmj/1408972906

Information

Published: July 2014
First available in Project Euclid: 25 August 2014

zbMATH: 1308.53075
MathSciNet: MR3251821
Digital Object Identifier: 10.32917/hmj/1408972906

Rights: Copyright © 2014 Hiroshima University, Mathematics Program

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Vol.44 • No. 2 • July 2014
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