{"title":"Sasakian 3流形中Legendre曲线的Legendre矩阵法","authors":"Tuba Ağirman Aydin, M. Sezer, H. Kocayiğit","doi":"10.2478/fcds-2021-0014","DOIUrl":null,"url":null,"abstract":"Abstract In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.","PeriodicalId":42909,"journal":{"name":"Foundations of Computing and Decision Sciences","volume":"46 1","pages":"205 - 219"},"PeriodicalIF":1.8000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold\",\"authors\":\"Tuba Ağirman Aydin, M. Sezer, H. Kocayiğit\",\"doi\":\"10.2478/fcds-2021-0014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.\",\"PeriodicalId\":42909,\"journal\":{\"name\":\"Foundations of Computing and Decision Sciences\",\"volume\":\"46 1\",\"pages\":\"205 - 219\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations of Computing and Decision Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/fcds-2021-0014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Computing and Decision Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/fcds-2021-0014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold
Abstract In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.
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