NONEMBEDDABILITY OF THE KLEIN BOTTLE IN RP 3 AND LAWSON’S CONJECTURE

Q2 Arts and Humanities
Oscar Perdomo
{"title":"NONEMBEDDABILITY OF THE KLEIN BOTTLE IN RP 3 AND LAWSON’S CONJECTURE","authors":"Oscar Perdomo","doi":"10.18257/raccefyn.29(110).2005.2151","DOIUrl":null,"url":null,"abstract":"In 1985 Montiel & Ros showed that the only minimal torus in S3 , for which the first eigenvalue of the Laplacian is 2, is the Clifford torus. Here, we will show first the nonexistence of an embedded Klein bottle in RP3 . Indeed we will prove that the only non orientable closed surfaces that can be embedded in RP3 are those with odd Euler characteristic. Later on, we will give another proof of Montiel & Ros’ result, assuming that the minimal torus has {x, –x} simmetry.","PeriodicalId":53418,"journal":{"name":"Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18257/raccefyn.29(110).2005.2151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0

Abstract

In 1985 Montiel & Ros showed that the only minimal torus in S3 , for which the first eigenvalue of the Laplacian is 2, is the Clifford torus. Here, we will show first the nonexistence of an embedded Klein bottle in RP3 . Indeed we will prove that the only non orientable closed surfaces that can be embedded in RP3 are those with odd Euler characteristic. Later on, we will give another proof of Montiel & Ros’ result, assuming that the minimal torus has {x, –x} simmetry.
rp - 3中克莱因瓶的不可嵌入性与劳森猜想
1985年Montiel &Ros证明了S3中唯一的最小环面是Clifford环面,其拉普拉斯的第一个特征值为2。在这里,我们将首先证明在RP3中不存在嵌入克莱因瓶。事实上,我们将证明RP3中唯一可嵌入的非定向封闭曲面是那些具有奇欧拉特征的曲面。稍后,我们将给出Montiel &Ros的结果,假设最小环面具有{x, -x}对称性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales
Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales Arts and Humanities-History and Philosophy of Science
CiteScore
0.90
自引率
0.00%
发文量
61
审稿时长
28 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信