{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T01:39:05Z","timestamp":1768268345766,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T00:00:00Z","timestamp":1745798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We introduced the concept of involute partner-ruled surfaces, which are formed by the involutes of spacelike curves and additional conditions ensuring the presence of definite surface normals in Minkowski three-space. First, we provided the criteria for each couple of involute partner-ruled surfaces to be simultaneously developable and minimal. Then, we established the requirements for the coordinate curves lying on these surfaces to be geodesic, asymptotic, and lines of curvature. We also expanded this paper with an example by providing graphical illustrations of the involute partner-ruled surfaces.<\/jats:p>","DOI":"10.3390\/axioms14050337","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"337","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Involute Partner-Ruled Surfaces Formed by Involutes of Spacelike Curves in Minkowski Three-Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1665-233X","authenticated-orcid":false,"given":"\u00d6zg\u00fcr","family":"Boyac\u0131o\u011flu Kalkan","sequence":"first","affiliation":[{"name":"Afyon Vocational School, Afyon Kocatepe University, 03200 Afyonkarahisar, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1097-5541","authenticated-orcid":false,"given":"S\u00fcleyman","family":"\u015eenyurt","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ordu University, 52200 Ordu, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0405-9969","authenticated-orcid":false,"given":"Davut","family":"Canl\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ordu University, 52200 Ordu, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0931-2054","authenticated-orcid":false,"given":"Luca","family":"Grilli","sequence":"additional","affiliation":[{"name":"Department of Economics, Management and Territory, University of Foggia, 71121 Foggia, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"From ruled surfaces to elastica-ruled surfaces: New possibilities for creating architectural forms","volume":"Volume 30","author":"Lee","year":"2020","journal-title":"Proceedings of IASS Annual Symposia"},{"key":"ref_2","first-page":"21","article-title":"Ruled surfaces in architecture","volume":"4","year":"2009","journal-title":"Int. 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[Ph.D. Thesis, Katholieke Universiteit]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/337\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:23:06Z","timestamp":1760030586000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/337"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,28]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050337"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050337","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,28]]}}}