Solitons of the mean curvature flow in $\mathbb{s}^2\times\mathbb{R}$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929252988878848 |
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| author | López, Rafael Munteanu, Marian Ioan |
| author_facet | López, Rafael Munteanu, Marian Ioan |
| contents | A soliton of the mean curvature flow in the product space $\mathbb{s}^2\times\mathbb{R}$ as a surface whose mean curvature $H$ satisfies the equation $H=\langle N,X\rangle$, where $N$ is the unit normal of the surface and $X$ is a Killing vector field. In this paper we consider the vector field tangent to the fibers and the vector field associated to a rotations about an axis of $\mathbb{s}^2$, respectively. We give a classification of the solitons with respect to these vector fields assuming that the surface is invariant under a one-parameter group of vertical translations or under a group of rotations of $\mathbb{s}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solitons of the mean curvature flow in $\mathbb{s}^2\times\mathbb{R}$ López, Rafael Munteanu, Marian Ioan Differential Geometry 53A10, 53C42, 53C44 A soliton of the mean curvature flow in the product space $\mathbb{s}^2\times\mathbb{R}$ as a surface whose mean curvature $H$ satisfies the equation $H=\langle N,X\rangle$, where $N$ is the unit normal of the surface and $X$ is a Killing vector field. In this paper we consider the vector field tangent to the fibers and the vector field associated to a rotations about an axis of $\mathbb{s}^2$, respectively. We give a classification of the solitons with respect to these vector fields assuming that the surface is invariant under a one-parameter group of vertical translations or under a group of rotations of $\mathbb{s}^2$. |
| title | Solitons of the mean curvature flow in $\mathbb{s}^2\times\mathbb{R}$ |
| topic | Differential Geometry 53A10, 53C42, 53C44 |
| url | https://arxiv.org/abs/2402.14727 |