{"title":"自展开式的刚性定理","authors":"Zhi Li, Guoxin Wei","doi":"10.1007/s00229-024-01573-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm <i>S</i> of the second fundamental form and constant <span>\\(f_{3}\\)</span> in the Euclidean space <span>\\({\\mathbb {R}}^{4}\\)</span>, where <span>\\(h_{ij}\\)</span> are components of the second fundamental form, <span>\\(S=\\sum _{i,j}h^{2}_{ij}\\)</span> and <span>\\(f_{3}=\\sum _{i,j,k}h_{ij}h_{jk}h_{ki}\\)</span>.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A rigidity theorem for self-expanders\",\"authors\":\"Zhi Li, Guoxin Wei\",\"doi\":\"10.1007/s00229-024-01573-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm <i>S</i> of the second fundamental form and constant <span>\\\\(f_{3}\\\\)</span> in the Euclidean space <span>\\\\({\\\\mathbb {R}}^{4}\\\\)</span>, where <span>\\\\(h_{ij}\\\\)</span> are components of the second fundamental form, <span>\\\\(S=\\\\sum _{i,j}h^{2}_{ij}\\\\)</span> and <span>\\\\(f_{3}=\\\\sum _{i,j,k}h_{ij}h_{jk}h_{ki}\\\\)</span>.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-024-01573-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01573-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm S of the second fundamental form and constant \(f_{3}\) in the Euclidean space \({\mathbb {R}}^{4}\), where \(h_{ij}\) are components of the second fundamental form, \(S=\sum _{i,j}h^{2}_{ij}\) and \(f_{3}=\sum _{i,j,k}h_{ij}h_{jk}h_{ki}\).
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