{"title":"基于达布框架的方向曲线生成的几种特殊直纹曲面及其特征","authors":"Nidal Echabbi, Amina Ouazzani Chahdi","doi":"10.1155/2021/8624794","DOIUrl":null,"url":null,"abstract":"In this work, we consider the Darboux frame \n \n \n \n T\n ,\n V\n ,\n U\n \n \n \n of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a \n \n V\n \n -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations\",\"authors\":\"Nidal Echabbi, Amina Ouazzani Chahdi\",\"doi\":\"10.1155/2021/8624794\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we consider the Darboux frame \\n \\n \\n \\n T\\n ,\\n V\\n ,\\n U\\n \\n \\n \\n of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a \\n \\n V\\n \\n -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.\",\"PeriodicalId\":7061,\"journal\":{\"name\":\"Abstract and Applied Analysis\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstract and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/8624794\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstract and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/8624794","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations
In this work, we consider the Darboux frame
T
,
V
,
U
of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a
V
-direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.
期刊介绍:
Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.