Invariant $λ$-translators in Lorentz-Minkowski space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909102149468160 |
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| author | Bueno, Antonio Ortiz, Irene |
| author_facet | Bueno, Antonio Ortiz, Irene |
| contents | Given $λ\in\mathbb{R}$ and $\textbf{v}\in\mathbb{L}^3$, a $λ$-translator with velocity $\textbf{v}$ is an immersed surface in $\mathbb{L}^3$ whose mean curvature satisfies $H=\langle N,\textbf{v}\rangle+λ$, where $N$ is a unit normal vector field. When $λ=0$, we fall into the class of translating solitons of the mean curvature flow. In this paper we study $λ$-translators in $\mathbb{L}^3$ that are invariant under a 1-parameter group of translations and rotations. The former are cylindrical surfaces and explicit parametrizations are found, distinguishing on the causality of both the ruling direction and the $λ$-translators. In the case of rotational $λ$-translators we distinguish between spacelike and timelike rotations and exhibit the qualitative properties of rotational $λ$-translators by analyzing the non-linear autonomous system fulfilled by the coordinate functions of the generating curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant $λ$-translators in Lorentz-Minkowski space Bueno, Antonio Ortiz, Irene Differential Geometry 53A10, 53C42, 34C05, 34C40 Given $λ\in\mathbb{R}$ and $\textbf{v}\in\mathbb{L}^3$, a $λ$-translator with velocity $\textbf{v}$ is an immersed surface in $\mathbb{L}^3$ whose mean curvature satisfies $H=\langle N,\textbf{v}\rangle+λ$, where $N$ is a unit normal vector field. When $λ=0$, we fall into the class of translating solitons of the mean curvature flow. In this paper we study $λ$-translators in $\mathbb{L}^3$ that are invariant under a 1-parameter group of translations and rotations. The former are cylindrical surfaces and explicit parametrizations are found, distinguishing on the causality of both the ruling direction and the $λ$-translators. In the case of rotational $λ$-translators we distinguish between spacelike and timelike rotations and exhibit the qualitative properties of rotational $λ$-translators by analyzing the non-linear autonomous system fulfilled by the coordinate functions of the generating curves. |
| title | Invariant $λ$-translators in Lorentz-Minkowski space |
| topic | Differential Geometry 53A10, 53C42, 34C05, 34C40 |
| url | https://arxiv.org/abs/2402.07237 |