{"title":"ℝ中的时样零均值曲率曲面1 4","authors":"Seher Kaya","doi":"10.1515/gmj-2024-2028","DOIUrl":null,"url":null,"abstract":"Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 \\mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Timelike zero mean curvature surfaces in ℝ1 4\",\"authors\":\"Seher Kaya\",\"doi\":\"10.1515/gmj-2024-2028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 \\\\mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2024-2028\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2028","RegionNum":4,"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
摘要
摘要 我们对 R 1 4 \mathbb{R}_{1}^{4} 中时间状曲面的比约林问题的解很感兴趣。本文的主要贡献在于提出了许多新的时样零均值曲率曲面的例子,并给出了它们的显式参数方程。在特殊情况下,我们会发现这些曲面的参数方程与洛伦兹-闵科夫斯基 3 空间中的时间极小曲面重合。
Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 \mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.
期刊介绍:
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.