Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913131751538688 |
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| author | Maeta, Shun |
| author_facet | Maeta, Shun |
| contents | In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile curve and then excluding all possible non-minimal branches. This is a partial affirmative answer to Chen's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09587 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal Maeta, Shun Differential Geometry 53C42, 53A07, 53B25 In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile curve and then excluding all possible non-minimal branches. This is a partial affirmative answer to Chen's conjecture. |
| title | Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal |
| topic | Differential Geometry 53C42, 53A07, 53B25 |
| url | https://arxiv.org/abs/2605.09587 |