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

Hashinaga Takahiro

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.

Lie groups

left-invariant Riemannian metrics

solvsolitons

symmetric spaces

minimal submanifolds

Mathematics [ 410 ]

eng

Copyright(c) by Author

Takahiro Hashinaga, On the minimality of the corresponding submanifolds to fourdimensional solvsolitons. Hiroshima Mathematical Journal (掲載決定) references

広島大学