{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:07Z","timestamp":1760241607529,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,13]],"date-time":"2018-06-13T00:00:00Z","timestamp":1528848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002531","name":"Kyungpook National University","doi-asserted-by":"publisher","award":["Bokhyeon Research Fund 2017"],"award-info":[{"award-number":["Bokhyeon Research Fund 2017"]}],"id":[{"id":"10.13039\/501100002531","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study ruled submanifolds in Minkowski space in regard to the Gauss map satisfying some partial differential equation. As a generalization of usual cylinders, cones and null scrolls in a three-dimensional Minkowski space, a cylinder over a space curve, a product manifold of a right cone and a k-plane, a product manifold of a hyperbolic cone and a k-plane which look like kinds of cylinders over cones in 3-space, and the generalized B-scroll kind in Minkowski space are characterized with the partial differential equation regarding the Gauss map, where k is a positive integer.<\/jats:p>","DOI":"10.3390\/sym10060218","type":"journal-article","created":{"date-parts":[[2018,6,15]],"date-time":"2018-06-15T10:15:14Z","timestamp":1529057714000},"page":"218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space"],"prefix":"10.3390","volume":"10","author":[{"given":"Sun Mi","family":"Jung","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Daegu 41566, Korea"}]},{"given":"Young Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Daegu 41566, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, B.-Y. (2015). Total Mean Curvature and Submanifolds of Finite Type, World Scientific. [2nd ed.].","DOI":"10.1142\/9237"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/BF01228047","article-title":"Ruled submanifolds with finite type Gauss map","volume":"49","author":"Baikoussis","year":"1994","journal-title":"J. Geom."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"341","DOI":"10.3836\/tjm\/1270128488","article-title":"Ruled surfaces and tubes with finite type Gauss map","volume":"16","author":"Baikoussis","year":"1993","journal-title":"Tokyo J. Math."},{"key":"ref_4","first-page":"117","article-title":"A report on submanifolds of finite type","volume":"22","author":"Chen","year":"1996","journal-title":"Soochow J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1017\/S0004972700028616","article-title":"Ruled surfaces of finite-type","volume":"42","author":"Chen","year":"1990","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1090\/S0002-9939-1992-1072333-5","article-title":"Ruled submanifolds of finite type","volume":"114","author":"Dillen","year":"1992","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1475","DOI":"10.11650\/twjm\/1500406744","article-title":"Some classification results on finite-type ruled submanifolds in a Lorentz-Minkowski space","volume":"16","author":"Kim","year":"2012","journal-title":"Taiwan. J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1016\/j.geomphys.2012.04.003","article-title":"Minimal ruled submanifolds in Minkowski space Lm","volume":"62","author":"Kim","year":"2012","journal-title":"J. Geom. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"53","DOI":"10.11650\/tjm.18.2014.3226","article-title":"Ruled submanifolds with harmonic Gauss map","volume":"18","author":"Kim","year":"2014","journal-title":"Taiwan. J. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.11650\/tjm.18.2014.3715","article-title":"Some classifications of ruled submanifolds in Minkowski space and their Gauss map","volume":"18","author":"Kim","year":"2014","journal-title":"Taiwan. J. Math."},{"key":"ref_11","first-page":"1","article-title":"Finite-type ruled surfaces in Lorentz-Minkowski space","volume":"11","author":"Kim","year":"2007","journal-title":"Taiwan. J. Math."},{"key":"ref_12","first-page":"1031","article-title":"Extended B-scrolls and their Gauss maps","volume":"33","author":"Kim","year":"2002","journal-title":"Indian J. Pure Appl. Math."},{"key":"ref_13","first-page":"1523","article-title":"Characterization of generalized B-scrolls and cylinders over finite-type curves","volume":"33","author":"Kim","year":"2003","journal-title":"Indian J. Pure Appl. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0393-0440(03)00084-6","article-title":"Classification of ruled surfaces in Minkowski 3-spaces","volume":"49","author":"Kim","year":"2004","journal-title":"J. Geom. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1216\/rmjm\/1181069651","article-title":"On the Gauss map of ruled surfaces in Minkowski space","volume":"35","author":"Kim","year":"2005","journal-title":"Rocky Mt. J. Math."},{"key":"ref_16","first-page":"753","article-title":"Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map","volume":"38","author":"Choi","year":"2001","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"203","DOI":"10.4064\/cm129-2-4","article-title":"Circular cone and its Gauss map","volume":"129","author":"Choi","year":"2012","journal-title":"Colloq. Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"447","DOI":"10.4134\/JKMS.2005.42.3.447","article-title":"Surfaces of revolution with pointwise 1-type Gauss map","volume":"42","author":"Chen","year":"2005","journal-title":"J. Korean Math. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.4134\/JKMS.j150498","article-title":"Gauss maps of ruled submanifolds and applications I","volume":"53","author":"Jung","year":"2016","journal-title":"J. Korean Math. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"227","DOI":"10.11650\/tjm.20.2016.5635","article-title":"Gauss maps of ruled submanifolds and applications II","volume":"20","author":"Kim","year":"2016","journal-title":"Taiwan. J. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.11650\/twjm\/1500405946","article-title":"Classification of ruled surfaces with pointwise 1-type Gauss map","volume":"14","author":"Choi","year":"2010","journal-title":"Taiwan. J. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.11650\/twjm\/1500406291","article-title":"Classification of ruled surfaces with pointwise 1-type Gauss map in Minkowski 3-space","volume":"15","author":"Choi","year":"2011","journal-title":"Taiwan. J. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4134\/JKMS.2009.46.1.215","article-title":"Helicoidal surfaces with pointwise 1-type Gauss map","volume":"46","author":"Choi","year":"2009","journal-title":"J. Korean Math. Soc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0393-0440(99)00063-7","article-title":"Ruled surfaces with pointwise 1-type Gauss maps","volume":"34","author":"Kim","year":"2000","journal-title":"J. Geom. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Karacan, M.K., Yuksel, N., and Ikiz, H. (2017). On ruled surface in 3-dimenional almost contact metric manifold. Int. J. Geom. Methods Mod. Phys., 14.","DOI":"10.1142\/S0219887817500761"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.difgeo.2016.11.007","article-title":"Sectional curvatures of ruled real hypersurfaces in complex hyperbolic spaces","volume":"51","author":"Maeda","year":"2017","journal-title":"Differ. Geom. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1550081","DOI":"10.1142\/S0219199715500819","article-title":"On generic submanifolds of manifolds endowed with metric mixed 3-structures","volume":"18","author":"Vilcu","year":"2016","journal-title":"Commun. Contemp. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"25","DOI":"10.2298\/PIM1715025A","article-title":"Ruled three-dimensional CR submanifolds of the sphere","volume":"101","author":"Miroslava","year":"2017","journal-title":"Publ. Inst. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"567","DOI":"10.11650\/tjm\/170908","article-title":"Minimal ruled submanifolds associated with Gauss map","volume":"22","author":"Jung","year":"2018","journal-title":"Taiwan. J. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1512\/iumj.1984.33.33028","article-title":"Minimal ruled submanifolds in spaces of constant curvature","volume":"33","author":"Barbosa","year":"1984","journal-title":"Indiana Univ. Math. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/218\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:08:36Z","timestamp":1760195316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/218"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,13]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["sym10060218"],"URL":"https:\/\/doi.org\/10.3390\/sym10060218","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,6,13]]}}}