Rotational surfaces with prescribed curvatures
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910592066912256 |
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| author | Carretero, Paula Castro, Ildefonso |
| author_facet | Carretero, Paula Castro, Ildefonso |
| contents | We solve the problem of prescribing different types of curvatures (principal, mean or Gaussian) on rotational surfaces in terms of arbitrary continuous functions depending on the distance from the surface to the axis of revolution. In this line, we get the complete explicit classification of the rotational surfaces with mean or Gauss curvature inversely proportional to the distance from the surface to the axis of revolution. We also provide new uniqueness results on some well known surfaces, such as the catenoid or the torus of revolution, and others less well known but equally interesting for their physical applications, such as the Mylar balloon or the Flamm's paraboloid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rotational surfaces with prescribed curvatures Carretero, Paula Castro, Ildefonso Differential Geometry 53A05, 53A04 We solve the problem of prescribing different types of curvatures (principal, mean or Gaussian) on rotational surfaces in terms of arbitrary continuous functions depending on the distance from the surface to the axis of revolution. In this line, we get the complete explicit classification of the rotational surfaces with mean or Gauss curvature inversely proportional to the distance from the surface to the axis of revolution. We also provide new uniqueness results on some well known surfaces, such as the catenoid or the torus of revolution, and others less well known but equally interesting for their physical applications, such as the Mylar balloon or the Flamm's paraboloid. |
| title | Rotational surfaces with prescribed curvatures |
| topic | Differential Geometry 53A05, 53A04 |
| url | https://arxiv.org/abs/2312.14672 |