{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:37:54Z","timestamp":1760150274700,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T00:00:00Z","timestamp":1697673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2023R337"],"award-info":[{"award-number":["PNURSP2023R337"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we have parameterized a timelike (Tlike) circular surface (CIsurface) and have obtained its geometric properties, including striction curves, singularities, Gaussian and mean curvatures. Afterward, the situation for a Tlike roller coaster surface (RCOsurface) to be a flat or minimal surface is examined in detail. Further, we illustrate the approach\u2019s outcomes with a number of pertinent examples.<\/jats:p>","DOI":"10.3390\/axioms12100989","type":"journal-article","created":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T07:15:36Z","timestamp":1697699736000},"page":"989","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Timelike Circular Surface and Singularities in Minkowski 3-Space"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7041-3730","authenticated-orcid":false,"given":"Areej A.","family":"Almoneef","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[[2023,10,19]]},"reference":[{"key":"ref_1","unstructured":"Carmo, M.P.D. (1976). Differential Geometry of Curves and Surfaces, Prentice-Hall."},{"key":"ref_2","unstructured":"Spivak, M.A. (1979). Comprehensive Introduction to Differential Geometry, Publish or Perish. [2nd ed.]."},{"key":"ref_3","unstructured":"Mc-Nertney, L.V. (1980). One-Parameter Families of Surfaces with Constant Curvature in Lorentz Three-Space. [Ph.D. Thesis, Brown University]."},{"key":"ref_4","unstructured":"Walfare, J. (1995). Curves and Surfaces in Minkowski Space. [Ph.D. Thesis, K.U. 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