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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.09708 |
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| _version_ | 1866915108871995392 |
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| author | Kislitsyn, Aleksei |
| author_facet | Kislitsyn, Aleksei |
| contents | A new approach for constructing minimal submanifolds of codimension 1 in the round spheres is proposed. In the case of $\mathbb{S}^3$ two immersions of the Clifford torus and all Lawson $τ_{n, m}$ surfaces are described in terms of $(λ, μ)$-eigenfunctions. Also, a new proof of a theorem that describes $(λ, μ)$-eigenfunctions on sphere is obtained. This proof is based on a statement that a function $f$ is a $(λ, μ)$-eigenfunction if and only if $f$ and $f^2$ are eigenfunctions for the Laplace-Beltrami operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal submanifolds in spheres and complex-valued eigenfunctions Kislitsyn, Aleksei Differential Geometry A new approach for constructing minimal submanifolds of codimension 1 in the round spheres is proposed. In the case of $\mathbb{S}^3$ two immersions of the Clifford torus and all Lawson $τ_{n, m}$ surfaces are described in terms of $(λ, μ)$-eigenfunctions. Also, a new proof of a theorem that describes $(λ, μ)$-eigenfunctions on sphere is obtained. This proof is based on a statement that a function $f$ is a $(λ, μ)$-eigenfunction if and only if $f$ and $f^2$ are eigenfunctions for the Laplace-Beltrami operator. |
| title | Minimal submanifolds in spheres and complex-valued eigenfunctions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.09708 |