On the governing equations of membrane O surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908605898293248 |
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| author | Jikumaru, Yoshiki |
| author_facet | Jikumaru, Yoshiki |
| contents | It is known that a shell membrane in equilibrium where a constant purely normal load $q_n$ acts on the membrane, and where the principal curvature lines coincide with the principal stress lines, forms an integrable system called a membrane O surface. This paper formulates the governing equations for membrane O surfaces of the 1st and 2nd kind, which are analogues to Guichard surfaces of the 1st and 2nd kind introduced by Calapso. Furthermore, under this formulation, we show that membrane O surfaces are a subclass of Demoulin's $Ω$ surfaces, and that the Bäcklund transformation for membrane O surfaces preserves membrane O surfaces of the 1st and 2nd kind, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the governing equations of membrane O surfaces Jikumaru, Yoshiki Differential Geometry 53A05, 53C42, 37K35, 74K15 It is known that a shell membrane in equilibrium where a constant purely normal load $q_n$ acts on the membrane, and where the principal curvature lines coincide with the principal stress lines, forms an integrable system called a membrane O surface. This paper formulates the governing equations for membrane O surfaces of the 1st and 2nd kind, which are analogues to Guichard surfaces of the 1st and 2nd kind introduced by Calapso. Furthermore, under this formulation, we show that membrane O surfaces are a subclass of Demoulin's $Ω$ surfaces, and that the Bäcklund transformation for membrane O surfaces preserves membrane O surfaces of the 1st and 2nd kind, respectively. |
| title | On the governing equations of membrane O surfaces |
| topic | Differential Geometry 53A05, 53C42, 37K35, 74K15 |
| url | https://arxiv.org/abs/2510.19284 |