{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:13Z","timestamp":1740165253647,"version":"3.37.3"},"reference-count":10,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"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":["11801065"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N2005012"],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"Based on the fundamental theories of null curves in Minkowski 3-space, the null Darboux mate curves of a null curve are defined which can be regarded as a kind of extension for Bertrand curves and Mannheim curves in Minkowski 3-space. The relationships of null Darboux curve pairs are explored and their expression forms are presented explicitly.<\/jats:p>","DOI":"10.3390\/axioms10030142","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T14:03:19Z","timestamp":1625061799000},"page":"142","source":"Crossref","is-referenced-by-count":2,"title":["Null Darboux Curve Pairs in Minkowski 3-Space"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6900-0426","authenticated-orcid":false,"given":"Jinhua","family":"Qian","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northeastern University, Shenyang 110004, China"}]},{"given":"Mingyu","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeastern University, Shenyang 110004, China"}]},{"given":"Pei","family":"Yin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeastern University, Shenyang 110004, China"}]},{"given":"Young-Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Daegu 41566, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1080\/0025570X.1960.11975181","article-title":"Bertrand curves associated with a pair of curves","volume":"34","author":"Burke","year":"1960","journal-title":"Math. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s00022-007-1949-0","article-title":"Mannheim partner curves in 3-Euclidean space","volume":"88","author":"Wang","year":"2008","journal-title":"J. Geom."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1016\/j.amc.2012.07.008","article-title":"Bertrand curves in 3-dimensional space forms","volume":"219","author":"Choi","year":"2012","journal-title":"Appl. Math. Comp."},{"key":"ref_4","first-page":"249","article-title":"On generalized spacelike Mannheim curves in Minkowski space-time","volume":"86","author":"Ilarslan","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.4134\/BKMS.2015.52.1.183","article-title":"Directional associated curves of a null curve in Minkowski 3-space","volume":"52","author":"Qian","year":"2015","journal-title":"Bull. Korean Math. 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[2nd ed.]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/142\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T21:54:05Z","timestamp":1720994045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":10,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["axioms10030142"],"URL":"https:\/\/doi.org\/10.3390\/axioms10030142","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,6,30]]}}}