{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:24:31Z","timestamp":1760059471398,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T00:00:00Z","timestamp":1750032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Recep Tayyip Erdo\u011fan University Development Foundation","award":["02025004007395"],"award-info":[{"award-number":["02025004007395"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce and develop the concept of osculating curve pairs in the three-dimensional Minkowski space. By defining a vector lying in the intersection of osculating planes of two non-lightlike curves, we characterize osculating mates based on their Frenet frames. We then derive the transformation matrix between these frames and investigate the curvature and torsion relations under varying causal characterizations of the curves\u2014timelike and spacelike. Furthermore, we determine the conditions under which these generalized osculating pairs reduce to well-known curve pairs such as Bertrand, Mannheim, and B\u00e4cklund pairs. Our results extend existing theories by unifying several known curve pair classifications under a single geometric framework in Lorentzian space.<\/jats:p>","DOI":"10.3390\/axioms14060468","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T09:51:22Z","timestamp":1750067482000},"page":"468","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Osculating Mate of a Curve in Minkowski 3-Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5674-8219","authenticated-orcid":false,"given":"\u0130skender","family":"\u00d6zt\u00fcrk","sequence":"first","affiliation":[{"name":"Department of Mathematics, Science and Art Center, Ministry of National Education, 07090 Antalya, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4317-7968","authenticated-orcid":false,"given":"Hasan","family":"\u00c7ak\u0131r","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Recep Tayyip Erdo\u011fan University, 53020 Rize, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1359-4181","authenticated-orcid":false,"given":"Mustafa","family":"\u00d6zdemir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Akdeniz University, 07070 Antalya, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,16]]},"reference":[{"key":"ref_1","unstructured":"O\u2019Neill, B. 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