球体中的Willmore曲面:通过共形高斯映射的DPW方法

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2019-07-09 DOI:10.1007/s12188-019-00204-9

Josef F. Dorfmeister, Peng Wang

{"title":"球体中的Willmore曲面:通过共形高斯映射的DPW方法","authors":"Josef F. Dorfmeister, Peng Wang","doi":"10.1007/s12188-019-00204-9","DOIUrl":null,"url":null,"abstract":"<div><p>The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in <span>\\({\\mathbb {R}}^{n+2}\\)</span>, isotropic surfaces in <span>\\(S^4\\)</span> and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in <span>\\(S^6\\)</span> without dual surfaces is also presented.\n</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-019-00204-9","citationCount":"6","resultStr":"{\"title\":\"Willmore surfaces in spheres: the DPW approach via the conformal Gauss map\",\"authors\":\"Josef F. Dorfmeister, Peng Wang\",\"doi\":\"10.1007/s12188-019-00204-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in <span>\\\\({\\\\mathbb {R}}^{n+2}\\\\)</span>, isotropic surfaces in <span>\\\\(S^4\\\\)</span> and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in <span>\\\\(S^6\\\\)</span> without dual surfaces is also presented.\\n</p></div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s12188-019-00204-9\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-019-00204-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-019-00204-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 6

摘要

本文通过保角高斯映射建立了Willmore曲面的DPW方法。作为应用，我们通过环群方法描述了\({\mathbb {R}}^{n+2}\)中的最小曲面、\(S^4\)中的各向同性曲面和均匀Willmore环面。给出了\(S^6\)中无对偶曲面的Willmore双球的一个新例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Willmore surfaces in spheres: the DPW approach via the conformal Gauss map

The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in \({\mathbb {R}}^{n+2}\), isotropic surfaces in \(S^4\) and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in \(S^6\) without dual surfaces is also presented.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.