{"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":"<div><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></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"693 - 704"},"PeriodicalIF":0.7000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01086-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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