New Examples of Translating Solitons in Generalised Robertson-Walker Geometries
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917216069353472 |
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| author | Artacho, Diego Lawn, Marie-Amélie Ortega, Miguel |
| author_facet | Artacho, Diego Lawn, Marie-Amélie Ortega, Miguel |
| contents | Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker spacetimes, due to their importance as Lorentzian manifolds, and because they admit a natural conformal Killing timelike vector field carrying substantial geometric information, which will play the role of this translating vector field. We identify three one-parameter families of warping functions for which these objects exist. As a first example of this notion of translator, we classify the analogues of the classical Grim Reapers within this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14529 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | New Examples of Translating Solitons in Generalised Robertson-Walker Geometries Artacho, Diego Lawn, Marie-Amélie Ortega, Miguel Differential Geometry 53C44, 53B30, 53C21, 53C42, 53C50 Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker spacetimes, due to their importance as Lorentzian manifolds, and because they admit a natural conformal Killing timelike vector field carrying substantial geometric information, which will play the role of this translating vector field. We identify three one-parameter families of warping functions for which these objects exist. As a first example of this notion of translator, we classify the analogues of the classical Grim Reapers within this context. |
| title | New Examples of Translating Solitons in Generalised Robertson-Walker Geometries |
| topic | Differential Geometry 53C44, 53B30, 53C21, 53C42, 53C50 |
| url | https://arxiv.org/abs/2211.14529 |