Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.15957 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910459095941120 |
|---|---|
| author | López, Rafael Munteanu, Marian Ioan |
| author_facet | López, Rafael Munteanu, Marian Ioan |
| contents | Translators in the special linear group $SL(2,\mathbb{R})$ are surfaces whose mean curvature $H$ and unit normal vector $N$ satisfy $H=\langle N,X\rangle$, where $X$ is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is $4$ and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Translators of the mean curvature flow in the special linear group $SL(2,\mathbb{R})$ López, Rafael Munteanu, Marian Ioan Differential Geometry Translators in the special linear group $SL(2,\mathbb{R})$ are surfaces whose mean curvature $H$ and unit normal vector $N$ satisfy $H=\langle N,X\rangle$, where $X$ is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is $4$ and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained. |
| title | Translators of the mean curvature flow in the special linear group $SL(2,\mathbb{R})$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.15957 |