{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T02:14:20Z","timestamp":1780539260212,"version":"3.54.1"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T00:00:00Z","timestamp":1672963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168"],"award-info":[{"award-number":["12101168"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LQ22A010014"],"award-info":[{"award-number":["LQ22A010014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["12101168"],"award-info":[{"award-number":["12101168"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LQ22A010014"],"award-info":[{"award-number":["LQ22A010014"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike circular surface is a one-parameter family of Lorentzian circles with a fixed radius regarding a non-null curve, which acts as the spine curve, and it has symmetrical properties. In the study, we have parametrized spacelike circular surfaces and have provided their geometric and singularity properties such as Gaussian and mean curvatures, comparing them with those of ruled surfaces and the classification of singularities. Furthermore, the conditions for spacelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we support the results of the approach with some examples.<\/jats:p>","DOI":"10.3390\/sym15010173","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T02:31:30Z","timestamp":1673231490000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Spacelike Circular Surfaces in Minkowski 3-Space"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311120, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maryam T.","family":"Aldossary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box-1982, Damam 31441, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rashad A.","family":"Abdel-Baky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Izumiya, S., and Takeuchi, N. (2001). Singularities of ruled surfaces in E3. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press.","DOI":"10.1017\/S0305004100004643"},{"key":"ref_2","unstructured":"Izumiya, S., and Takeuchi, N. (2003). Geometry of ruled surfaces. Appl. Math. Gold. 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