Genus two embedded minimal surfaces in $\mathbb{S}^3$ with bidihedral symmetry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914255925673984 |
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| author | Espinar, José M. Pérez, Joaquín |
| author_facet | Espinar, José M. Pérez, Joaquín |
| contents | The isometry group of the classical Lawson embedded minimal surface $ξ_{2,1}\subset \mathbb{S}^3$ of genus 2 is isomorphic to the product $S_3\times D_4$ of the permutation group of three elements and the dihedral group of order 8 (symmetries of a square). $S_3\times D_4$ has a subgroup of index 3 isomorphic to the bidihedral group $D_{4h}=\mathbb{Z}_2\times D_4$, where $D_4$ is the dihedral group of order 8. We prove that $ξ_{2,1}$ is the unique closed embedded minimal surface of genus 2 in $\mathbb{S}^3$ whose isometry group contains $D_{4h}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_16295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Genus two embedded minimal surfaces in $\mathbb{S}^3$ with bidihedral symmetry Espinar, José M. Pérez, Joaquín Differential Geometry Primary 53A10, Secondary 49Q05, 53C42 The isometry group of the classical Lawson embedded minimal surface $ξ_{2,1}\subset \mathbb{S}^3$ of genus 2 is isomorphic to the product $S_3\times D_4$ of the permutation group of three elements and the dihedral group of order 8 (symmetries of a square). $S_3\times D_4$ has a subgroup of index 3 isomorphic to the bidihedral group $D_{4h}=\mathbb{Z}_2\times D_4$, where $D_4$ is the dihedral group of order 8. We prove that $ξ_{2,1}$ is the unique closed embedded minimal surface of genus 2 in $\mathbb{S}^3$ whose isometry group contains $D_{4h}$. |
| title | Genus two embedded minimal surfaces in $\mathbb{S}^3$ with bidihedral symmetry |
| topic | Differential Geometry Primary 53A10, Secondary 49Q05, 53C42 |
| url | https://arxiv.org/abs/2511.16295 |