{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:29Z","timestamp":1753881269689,"version":"3.41.2"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,10,15]],"date-time":"2012-10-15T00:00:00Z","timestamp":1350259200000},"content-version":"vor","delay-in-days":288,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100007278","name":"National University of Sciences and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007278","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (<jats:italic>n<\/jats:italic> \u2212 1)\u2010area enclosing a constant <jats:italic>n<\/jats:italic>\u2010volume in a Euclidean space is <jats:italic>s<\/jats:italic><jats:italic>o<\/jats:italic>(<jats:italic>n<\/jats:italic>)\u2295<jats:sub><jats:italic>s<\/jats:italic><\/jats:sub><jats:italic>\u211d<\/jats:italic><jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> and in a space of constant curvature the Lie algebra is <jats:italic>s<\/jats:italic><jats:italic>o<\/jats:italic>(<jats:italic>n<\/jats:italic>). Furthermore, if the space has one section of constant curvature of dimension <jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub>, another of <jats:italic>n<\/jats:italic><jats:sub>2<\/jats:sub>, and so on to <jats:italic>n<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> and one of zero curvature of dimension <jats:italic>m<\/jats:italic>, with  (as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is .<\/jats:p>","DOI":"10.1155\/2012\/532690","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T09:04:55Z","timestamp":1350378295000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Noether Symmetries of the Area\u2010Minimizing Lagrangian"],"prefix":"10.1155","volume":"2012","author":[{"given":"Adnan","family":"Aslam","sequence":"first","affiliation":[]},{"given":"Asghar","family":"Qadir","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"volume-title":"Differential Equations: Their Solutions Using Symmetry","year":"1989","author":"Stephani H.","key":"e_1_2_10_1_2"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68028-6"},{"volume-title":"Elementary Lie Group Analysis and Ordinary Differential Equations","year":"1999","author":"Ibragimov N. 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