{"title":"欧几里德n空间中两个参数曲面的相交曲线","authors":"M. Düldül, Merih Özçetin","doi":"10.12697/acutm.2021.25.17","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"97 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Intersection curve of two parametric surfaces in Euclidean n-space\",\"authors\":\"M. Düldül, Merih Özçetin\",\"doi\":\"10.12697/acutm.2021.25.17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.\",\"PeriodicalId\":42426,\"journal\":{\"name\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"volume\":\"97 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12697/acutm.2021.25.17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta et Commentationes Universitatis Tartuensis de Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12697/acutm.2021.25.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Intersection curve of two parametric surfaces in Euclidean n-space
The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.
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