{"title":"沿方向曲线的曲面的法线可展曲面","authors":"Rashad Abdel-Baky Abdel-Sattar, Y. Ünlütürk","doi":"10.22342/JIMS.26.3.872.319-333","DOIUrl":null,"url":null,"abstract":"We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Normal Developable Surfaces of A Surface Along A Direction Curve\",\"authors\":\"Rashad Abdel-Baky Abdel-Sattar, Y. Ünlütürk\",\"doi\":\"10.22342/JIMS.26.3.872.319-333\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.\",\"PeriodicalId\":42206,\"journal\":{\"name\":\"Journal of the Indonesian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Indonesian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22342/JIMS.26.3.872.319-333\",\"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":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/JIMS.26.3.872.319-333","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Normal Developable Surfaces of A Surface Along A Direction Curve
We construct a developable surface normal to a surface along a curve on the surface. As differs from the work Hananoi, we choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.
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