{"title":"论欧几里得三空间中任何正则曲线的主教框","authors":"Sümeyye GÜR MAZLUM","doi":"10.35414/akufemubid.1343172","DOIUrl":null,"url":null,"abstract":"Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.","PeriodicalId":7433,"journal":{"name":"Afyon Kocatepe University Journal of Sciences and Engineering","volume":"46 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Bishop Frames of Any Regular Curve in Euclidean 3-Space\",\"authors\":\"Sümeyye GÜR MAZLUM\",\"doi\":\"10.35414/akufemubid.1343172\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.\",\"PeriodicalId\":7433,\"journal\":{\"name\":\"Afyon Kocatepe University Journal of Sciences and Engineering\",\"volume\":\"46 5\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afyon Kocatepe University Journal of Sciences and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35414/akufemubid.1343172\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afyon Kocatepe University Journal of Sciences and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35414/akufemubid.1343172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Bishop Frames of Any Regular Curve in Euclidean 3-Space
Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.
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