论各向同性平面内曲线的演变

Pub Date : 2024-05-25 DOI:10.1007/s00010-024-01086-w

R. Pacheco, S. D. Santos

{"title":"论各向同性平面内曲线的演变","authors":"R. Pacheco, S. D. Santos","doi":"10.1007/s00010-024-01086-w","DOIUrl":null,"url":null,"abstract":"<p>We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On evolutes of curves in the isotropic plane\",\"authors\":\"R. Pacheco, S. D. Santos\",\"doi\":\"10.1007/s00010-024-01086-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-25\",\"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/s00010-024-01086-w\",\"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/s00010-024-01086-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们将各向同性平面中的每条空间曲线与洛伦兹三维空间中的一条空曲线联系起来。我们将前者的各向同性几何与后者的洛伦兹几何联系起来。我们证明了各向同性平面内曲线的泰特-克内瑟（Tait-Kneser）定理的一个版本。我们给出了一些明确的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

On evolutes of curves in the isotropic plane

We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.

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