{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:36:21Z","timestamp":1760229381269,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T00:00:00Z","timestamp":1654732800000},"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","LQ22A010014"],"award-info":[{"award-number":["12101168","LQ22A010014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural","doi-asserted-by":"publisher","award":["12101168","LQ22A010014"],"award-info":[{"award-number":["12101168","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>Bertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of 1,3-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be 1,3-V Bertrand curves. Some related examples are given.<\/jats:p>","DOI":"10.3390\/sym14061191","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T02:01:44Z","timestamp":1655085704000},"page":"1191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["A New Class of Bertrand Curves in Euclidean 4-Space"],"prefix":"10.3390","volume":"14","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 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"U\u00e7um","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, K\u0131r\u0131kkale University, 71450 K\u0131r\u0131kkale, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaz\u0131m","family":"\u0130larslan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, K\u0131r\u0131kkale University, 71450 K\u0131r\u0131kkale, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c7etin","family":"Camc\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, Onsekiz Mart University, 17100 \u00c7anakkale, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,9]]},"reference":[{"key":"ref_1","unstructured":"Kuhnel, W. 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