A new family of translating solitons in hyperbolic space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910322617483264 |
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| author | Bueno, Antonio López, Rafael |
| author_facet | Bueno, Antonio López, Rafael |
| contents | If $ξ$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $Σ\subset\h^3$ is a $ξ$-translator if its mean curvature $H$ satisfies $H=\langle N,ξ\rangle$, where $N$ is the unit normal of $Σ$. We classify all $ξ$-translators invariant by a one-parameter group of rotations of $\h^3$, exhibiting the existence of a new family of grim reapers. We use these grim reapers to prove the non-existence of closed $ξ$-translators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new family of translating solitons in hyperbolic space Bueno, Antonio López, Rafael Differential Geometry 53A10, 53C44, 53C21, 53C4 If $ξ$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $Σ\subset\h^3$ is a $ξ$-translator if its mean curvature $H$ satisfies $H=\langle N,ξ\rangle$, where $N$ is the unit normal of $Σ$. We classify all $ξ$-translators invariant by a one-parameter group of rotations of $\h^3$, exhibiting the existence of a new family of grim reapers. We use these grim reapers to prove the non-existence of closed $ξ$-translators. |
| title | A new family of translating solitons in hyperbolic space |
| topic | Differential Geometry 53A10, 53C44, 53C21, 53C4 |
| url | https://arxiv.org/abs/2402.05533 |