{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T12:15:49Z","timestamp":1767183349040,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,14]],"date-time":"2016-11-14T00:00:00Z","timestamp":1479081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education","award":["2015R1D1A1A01060046"],"award-info":[{"award-number":["2015R1D1A1A01060046"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, we study helicoidal surfaces in the three-dimensional isotropic space     I 3     and construct helicoidal surfaces satisfying a linear equation in terms of the Gaussian curvature and the mean curvature of the surface.<\/jats:p>","DOI":"10.3390\/sym8110126","type":"journal-article","created":{"date-parts":[[2016,11,14]],"date-time":"2016-11-14T11:39:50Z","timestamp":1479123590000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Linear Weingarten Helicoidal Surfaces in Isotropic Space"],"prefix":"10.3390","volume":"8","author":[{"given":"Dae","family":"Yoon","sequence":"first","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jae","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,14]]},"reference":[{"key":"ref_1","first-page":"382","article-title":"\u00dcber eine Klasse auf einander abwickelbarer Fl\u00e4chen","volume":"59","author":"Weingarten","year":"1861","journal-title":"J. Reine Angew. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.geomphys.2009.12.013","article-title":"Ruled Weingarten hypersurfaces in the Lorentz-Minkowski space and in de Sitter space","volume":"60","author":"Asperti","year":"2010","journal-title":"J. Geom. Phys."},{"key":"ref_3","unstructured":"Aydin, M.E., and \u00d6\u011frenmi\u015f, A.O. (2016). Linear Weingarten Factorable Surfaces in Isotropic Spaces, Cornell University Library."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s11856-012-0053-9","article-title":"Rotational linear Weingarten surfaces into the Euclidean sphere","volume":"192","author":"Barros","year":"2012","journal-title":"Isr. J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1515\/advgeom-2015-0040","article-title":"Classes of generalized Weingarten surfaces in the Euclidean 3-space","volume":"16","author":"Dias","year":"2016","journal-title":"Adv. Geom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"507","DOI":"10.12732\/ijam.v28i5.4","article-title":"On a certain class of Weingarten surfaces in Sol space","volume":"28","author":"Erjavec","year":"2015","journal-title":"Int. J. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00605-002-0510-3","article-title":"Linear Weingarten surfaces in R3","volume":"138","year":"2003","journal-title":"Mon. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"405210","DOI":"10.1088\/1751-8113\/43\/40\/405210","article-title":"On the invariant theory of Weingarten surfaces in Euclidean space","volume":"43","author":"Ganchev","year":"2010","journal-title":"J. Phys. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.jmaa.2005.06.032","article-title":"Helicoidal surfaces under the cubic screw motion in Minkowski 3-space","volume":"318","author":"Ji","year":"2006","journal-title":"J. Math. Anal. Appl."},{"key":"ref_10","first-page":"479","article-title":"Weingarten quadric surfaces in a Euclidean 3-space","volume":"35","author":"Kim","year":"2011","journal-title":"Turk. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s00605-005-0313-4","article-title":"On closed Weingarten surfaces","volume":"146","author":"Steller","year":"2005","journal-title":"Mon. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1142\/S0129167X08004728","article-title":"On linear Weingarten surfaces","volume":"19","year":"2008","journal-title":"Int. J. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00209-012-1010-3","article-title":"Classification of rotational special Weingarten surfaces of minimal type in S2 \u00d7 R and H2 \u00d7 R","volume":"273","author":"Morabito","year":"2013","journal-title":"Math. Z."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.4064\/ap107-1-4","article-title":"Non-degenerate quadric surfaces of Weingarten type","volume":"107","author":"Yoon","year":"2013","journal-title":"Ann. Pol. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s10444-008-9076-5","article-title":"Laguerre minimal surfaces, isotropic geometry and linear elasticity","volume":"31","author":"Pottmann","year":"2009","journal-title":"Adv. Copmut. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/s10998-014-0027-2","article-title":"Translation surfaces of constant curvatures in a simpley isotropic space","volume":"68","year":"2014","journal-title":"Period. Math. Hung."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Aydin, M.E. (2016). Classification Results on Surfaces in the Isotropic 3-Space, Cornell University Library.","DOI":"10.5578\/fmbd.27735"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1515\/phys-2016-0030","article-title":"Rotational surfaces in isotropic spaces satisfying weingarten conditions","volume":"14","year":"2016","journal-title":"Open Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/8\/11\/126\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:35:28Z","timestamp":1760211328000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/8\/11\/126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,14]]},"references-count":18,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2016,11]]}},"alternative-id":["sym8110126"],"URL":"https:\/\/doi.org\/10.3390\/sym8110126","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2016,11,14]]}}}