{"title":"Dual Cartan numbers and pseudo-null lines","authors":"İskender Öztürk","doi":"10.1002/mma.10323","DOIUrl":null,"url":null,"abstract":"<p>The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number with lightlike dual vector also corresponds to a parabolic rotation and a translation transformation in the Cartan frame. Also, the angle between the directed pseudo-null lines that tangent the same parabola is defined. Thus, the rotation and translation relationship between two directed pseudo-null lines is obtained. Also, the E. Study transformation is given for the directed pseudo-null lines.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 1","pages":"207-217"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10323","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number with lightlike dual vector also corresponds to a parabolic rotation and a translation transformation in the Cartan frame. Also, the angle between the directed pseudo-null lines that tangent the same parabola is defined. Thus, the rotation and translation relationship between two directed pseudo-null lines is obtained. Also, the E. Study transformation is given for the directed pseudo-null lines.
本研究旨在介绍对偶卡当数的一些几何性质。由于具有类光向量部分的单位时间卡当数对应于绕类光轴线的抛物线旋转，因此证明了具有类光对偶向量的单位对偶卡当数也对应于在卡当框架中的抛物线旋转和平移变换。此外，还定义了与同一抛物线相切的有向伪零线之间的夹角。因此，可以得到两条有向伪零线之间的旋转和平移关系。此外，还给出了有向伪零线的 E. Study 变换。
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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