f-left-invariant Riemannian metrics on Lie groups
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2014
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910351286599680 |
|---|---|
| author | Moghaddam, Hamid Reza Salimi |
| author_facet | Moghaddam, Hamid Reza Salimi |
| contents | With a f-left-invariant Riemannian metric on a Lie group $G$, we mean a Riemannian metric which is conformally equivalent to a left-invariant Riemannian metric, with the conformal factor $f$. In this article, we study the geometry of such metrics and give a necessary and sufficient condition for an f-left-invariant Riemannian metric to be a Ricci soliton. Using this result, for any expansion constant $λ$, we obtain a flat gradient Ricci soliton on some two and three-dimensional non-abelian Lie groups. We give an example of a non-flat steady gradient Ricci soliton and construct some examples of non-flat shrinking, steady, and expanding non-gradient Ricci solitons on the non-abelian Lie group $\Bbb{R}\rtimes\Bbb{R}^{+}$. Finally, we study f-left-invariant Riemannian metrics on the Heisenberg group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1401_0744 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | f-left-invariant Riemannian metrics on Lie groups Moghaddam, Hamid Reza Salimi Differential Geometry 53C30, 53C21, 22E60 With a f-left-invariant Riemannian metric on a Lie group $G$, we mean a Riemannian metric which is conformally equivalent to a left-invariant Riemannian metric, with the conformal factor $f$. In this article, we study the geometry of such metrics and give a necessary and sufficient condition for an f-left-invariant Riemannian metric to be a Ricci soliton. Using this result, for any expansion constant $λ$, we obtain a flat gradient Ricci soliton on some two and three-dimensional non-abelian Lie groups. We give an example of a non-flat steady gradient Ricci soliton and construct some examples of non-flat shrinking, steady, and expanding non-gradient Ricci solitons on the non-abelian Lie group $\Bbb{R}\rtimes\Bbb{R}^{+}$. Finally, we study f-left-invariant Riemannian metrics on the Heisenberg group. |
| title | f-left-invariant Riemannian metrics on Lie groups |
| topic | Differential Geometry 53C30, 53C21, 22E60 |
| url | https://arxiv.org/abs/1401.0744 |