{"title":"E^3中基于Frenet框架的带Darboux矢量的smarandache直纹曲面","authors":"S. Şenyurt, Davut Canlı, Elif Çan","doi":"10.53570/jnt.1106331","DOIUrl":null,"url":null,"abstract":"The paper introduces a new kind of special ruled surface. The base of each ruled surface is taken to be one of the Smarandache curves of a given curve according to Frenet frame, and the generator (ruling) is chosen to be the corresponding unit Darboux vector. The characteristics of these newly defined ruled surfaces are investigated by means of first and second fundamental forms and their corresponding curvatures. An example is provided by considering both the helix curve and the Viviani’s curve.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Smarandache-Based Ruled Surfaces with the Darboux Vector According to Frenet Frame in $E^3$\",\"authors\":\"S. Şenyurt, Davut Canlı, Elif Çan\",\"doi\":\"10.53570/jnt.1106331\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper introduces a new kind of special ruled surface. The base of each ruled surface is taken to be one of the Smarandache curves of a given curve according to Frenet frame, and the generator (ruling) is chosen to be the corresponding unit Darboux vector. The characteristics of these newly defined ruled surfaces are investigated by means of first and second fundamental forms and their corresponding curvatures. An example is provided by considering both the helix curve and the Viviani’s curve.\",\"PeriodicalId\":347850,\"journal\":{\"name\":\"Journal of New Theory\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of New Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.53570/jnt.1106331\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of New Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53570/jnt.1106331","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Smarandache-Based Ruled Surfaces with the Darboux Vector According to Frenet Frame in $E^3$
The paper introduces a new kind of special ruled surface. The base of each ruled surface is taken to be one of the Smarandache curves of a given curve according to Frenet frame, and the generator (ruling) is chosen to be the corresponding unit Darboux vector. The characteristics of these newly defined ruled surfaces are investigated by means of first and second fundamental forms and their corresponding curvatures. An example is provided by considering both the helix curve and the Viviani’s curve.
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