Maximal translation surfaces in Lorentz-Minkowski space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915398202425344 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | A translation surface in Lorentz-Minkowski space $\rr^3$ is a surface defined as the sum of two spatial curves. In this paper we present a classification of maximal surfaces of translation type. We prove that if a generating curve is planar, then the other generating curve is also planar. We give a full description of these surfaces. In case that both curves are of Frenet type, we generalize the Scherk surfaces. In case that a curve is a pseudo-null curve, we obtain new examples of maximal surfaces which have not counterparts in Euclidean space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_14103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal translation surfaces in Lorentz-Minkowski space López, Rafael Differential Geometry 53A10, 53C42, 53C50 A translation surface in Lorentz-Minkowski space $\rr^3$ is a surface defined as the sum of two spatial curves. In this paper we present a classification of maximal surfaces of translation type. We prove that if a generating curve is planar, then the other generating curve is also planar. We give a full description of these surfaces. In case that both curves are of Frenet type, we generalize the Scherk surfaces. In case that a curve is a pseudo-null curve, we obtain new examples of maximal surfaces which have not counterparts in Euclidean space. |
| title | Maximal translation surfaces in Lorentz-Minkowski space |
| topic | Differential Geometry 53A10, 53C42, 53C50 |
| url | https://arxiv.org/abs/2507.14103 |