{"title":"根据正则曲线的Frenet-Serret框架的Smarandache直纹曲面","authors":"Soukaina Ouarab","doi":"10.1155/2021/5526536","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in \n \n \n \n E\n \n \n 3\n \n \n \n . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in \\n \\n \\n E\\n \\n \\n 3\",\"authors\":\"Soukaina Ouarab\",\"doi\":\"10.1155/2021/5526536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in \\n \\n \\n \\n E\\n \\n \\n 3\\n \\n \\n \\n . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.\",\"PeriodicalId\":7061,\"journal\":{\"name\":\"Abstract and Applied Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstract and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/5526536\",\"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/10.1155/2021/5526536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in
E
3
In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in
E
3
. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.
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.
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