{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T14:30:07Z","timestamp":1761921007468,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:00:00Z","timestamp":1648512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obtained. In particular, we mostly focused on the study of the resulting developable surface is a cylinder, cone, or tangent surface. Meanwhile, to support the results in the paper, some illustrative examples are presented.<\/jats:p>","DOI":"10.3390\/sym14040698","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T21:45:51Z","timestamp":1648590351000},"page":"698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Sweeping Surfaces in theThree-Dimensional Lie Group"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3593-3244","authenticated-orcid":false,"given":"Sahar H.","family":"Nazra","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 24382, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7016-9280","authenticated-orcid":false,"given":"Rashad A.","family":"Abdel-Baky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"535123","DOI":"10.1155\/2012\/535123","article-title":"General helices of AW (k)-type in the Lie group","volume":"2012","author":"Yoon","year":"2012","journal-title":"J. Appl. Math."},{"key":"ref_2","first-page":"81","article-title":"On curves of constant breadth in a 3-dimensional Lie group","volume":"85","author":"Yoon","year":"2016","journal-title":"Acta Math. Univ. Comen."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"503","DOI":"10.12988\/ijma.2016.6230","article-title":"Classifications of special curves in the Three-Dimensional Lie Group","volume":"10","author":"Yoon","year":"2016","journal-title":"Int. J. Math. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1007\/s00006-016-0651-4","article-title":"Spinor Frenet equations in three dimensional Lie Groups","volume":"26","author":"Okuyucu","year":"2016","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s00022-019-0487-x","article-title":"On constructions of surfaces using a geodesic in Lie group","volume":"110","author":"Yoon","year":"2019","journal-title":"J. Geom."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cakmak, A. (2019). New type direction curves in 3-dimensional compact Lie group. Symmetry, 11.","DOI":"10.3390\/sym11030387"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"444","DOI":"10.15672\/hujms.664764","article-title":"A generalization for surfaces using a line of curvature in Lie group","volume":"50","author":"Yoon","year":"2021","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_8","unstructured":"Do Carmo, M.P. (1976). Differential Geometry of Curves and Surfaces, Prentice Hall."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Pottmann, H., and Wallner, J. (2001). Computational Line Geometry, Springer.","DOI":"10.1007\/978-3-642-04018-4"},{"key":"ref_10","first-page":"1","article-title":"Computation of rotating minimizing frames","volume":"27","author":"Wang","year":"2008","journal-title":"ACM Trans. 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Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2150184","DOI":"10.1142\/S1793557121501849","article-title":"Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space","volume":"14","author":"Mofarreh","year":"2021","journal-title":"Asian-Eur. J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.pnsc.2007.09.001","article-title":"A new method for designing a developable surface utilizing the surface pencil through a given curve","volume":"18","author":"Zhao","year":"2008","journal-title":"Prog. Nat. 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