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Simple factor dressing and the López–Ros deformation of minimal surfaces in Euclidean 3-space
http://hdl.handle.net/2241/00157287
http://hdl.handle.net/2241/00157287aeb2554e-38f9-449d-8196-3796539f58b0
名前 / ファイル | ライセンス | アクション |
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MZ_291-1015 (3.0 MB)
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Item type | Journal Article(1) | |||||
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公開日 | 2019-08-08 | |||||
タイトル | ||||||
タイトル | Simple factor dressing and the López–Ros deformation of minimal surfaces in Euclidean 3-space | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
守屋, 克洋
× 守屋, 克洋× Leschke, K. |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | The aim of this paper is to investigate a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3-space is a Willmore surface, its conformal Gauss map is harmonic and a dressing on the conformal Gauss map can be defined. We study the induced transformation on minimal surfaces in the simplest case, the simple factor dressing, and show that the well-known López–Ros deformation of minimal surfaces is a special case of this transformation. We express the simple factor dressing and the López–Ros deformation explicitly in terms of the minimal surface and its conjugate surface. In particular, we can control periods and end behaviour of the simple factor dressing. This allows to construct new examples of doubly-periodic minimal surfaces arising as simple factor dressings of Scherk’s first surface. | |||||
書誌情報 |
Mathematische Zeitschrift 巻 291, 号 3-4, p. 1015-1058, 発行日 2018-12 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0025-5874 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0072420X | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1007/s00209-018-2217-8 | |||||
権利 | ||||||
権利情報 | © The Author(s) 2018 | |||||
権利 | ||||||
権利情報 | This article is distributed under the terms of the Creative Commons Attribution 4.0 InternationalLicense(http://creativecommons.org/licenses/by/4.0/),whichpermitsunrestricteduse,distribution,andrepro-duction in any medium, provided you give appropriate credit to the original author(s) and the source, providea link to the Creative Commons license, and indicate if changes were made. | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | Springer Nature |