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ID 35939
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title alternative
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
creator
subject
Lie groups
left-invariant Riemannian metrics
solvsolitons
symmetric spaces
minimal submanifolds
NDC
Mathematics
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 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.
language
eng
nii type
Thesis or Dissertation
HU type
Doctoral Theses
DCMI type
text
format
application/pdf
text version
ETD
rights
Copyright(c) by Author
relation references
Takahiro Hashinaga, On the minimality of the corresponding submanifolds to fourdimensional solvsolitons. Hiroshima Mathematical Journal (掲載決定)
grantid
甲第6358号
degreeGrantor
広島大学(Hiroshima University)
degreename Ja
博士(理学)
degreename En
Science
degreelevel
doctoral
date of granted
2014-03-23
department
Graduate School of Science