{"title":"欧几里得三维空间E³中曲面中心曲线的扫面","authors":"R. Abdel-Baky, F. Mofarreh","doi":"10.37394/23206.2021.20.24","DOIUrl":null,"url":null,"abstract":"For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced. Key-Words: Darboux frame, Sweeping surface, Singularity.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Sweeping surface of center curve on surface in Euclidean 3-space E³\",\"authors\":\"R. Abdel-Baky, F. Mofarreh\",\"doi\":\"10.37394/23206.2021.20.24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced. Key-Words: Darboux frame, Sweeping surface, Singularity.\",\"PeriodicalId\":112268,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics archive\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics archive\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2021.20.24\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics archive","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2021.20.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sweeping surface of center curve on surface in Euclidean 3-space E³
For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced. Key-Words: Darboux frame, Sweeping surface, Singularity.
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