{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:56Z","timestamp":1760240696498,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T00:00:00Z","timestamp":1566864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2019R1C1C1006370"],"award-info":[{"award-number":["NRF-2019R1C1C1006370"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Gauss map. Concerning integrability and geometry, we set up new characterizations of the Clifford torus and the great sphere of 3-sphere and construct new examples of spherical ruled surfaces in a three-dimensional sphere.<\/jats:p>","DOI":"10.3390\/sym11091076","type":"journal-article","created":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T11:13:30Z","timestamp":1566904410000},"page":"1076","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Characterizations of the Clifford Torus and the Great Sphere"],"prefix":"10.3390","volume":"11","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"}]},{"given":"Jinhua","family":"Qian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeastern University, Shenyang 110004, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"380","DOI":"10.2969\/jmsj\/01840380","article-title":"Minimal immersions of Riemannian manifolds","volume":"18","author":"Takahashi","year":"1966","journal-title":"J. Math. Soc. Jpn."},{"unstructured":"Chen, B.-Y. (1985). Finite-Type Submanifolds and Generalizations, Instituto \u201cGuido Castelnuovo\u201d.","key":"ref_2"},{"key":"ref_3","first-page":"243","article-title":"Surfaces of finite-type in Euclidean 3-space","volume":"39","author":"Chen","year":"1987","journal-title":"Bull. Soc. Math. Belg."},{"key":"ref_4","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_5","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_6","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_7","first-page":"197","article-title":"On non-developable ruled surfaces in Lorentz-Minkowski 3-spaces","volume":"11","author":"Kim","year":"2007","journal-title":"Taiwan. J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BF01222665","article-title":"A classification of ruled surfaces of finite type in S3","volume":"50","author":"Hasanis","year":"1994","journal-title":"J. Geom."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1017\/S0004972700013162","article-title":"Submanifolds with finite-type Gauss map","volume":"35","author":"Chen","year":"1987","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1017\/S0017089500008946","article-title":"On the Gauss map of ruled surfaces","volume":"34","author":"Baikoussis","year":"1992","journal-title":"Glasg. Math. J."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"388","DOI":"10.2996\/kmj\/1138043655","article-title":"Surfaces with 1-tpye Gauss map","volume":"19","author":"Jang","year":"1996","journal-title":"Kodai Math. J."},{"key":"ref_14","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_15","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_16","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_17","first-page":"85","article-title":"Ruled surfaces with finite type Gauss map in Minkowski spaces","volume":"26","author":"Kim","year":"2000","journal-title":"Soochow J. 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","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."},{"doi-asserted-by":"crossref","unstructured":"Choi, M., Kim, D.-S., Kim, Y.H., and Yoon, D.W. (2012). Circular cone and its Gauss map. Colloq. Math., 129.","key":"ref_20","DOI":"10.4064\/cm129-2-4"},{"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":"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_23","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_24","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."},{"doi-asserted-by":"crossref","unstructured":"Jung, S.M., and Kim, Y.H. (2018). Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space. Symmetry, 10.","key":"ref_25","DOI":"10.3390\/sym10060218"},{"key":"ref_26","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_27","doi-asserted-by":"crossref","first-page":"217","DOI":"10.4310\/jdg\/1214428258","article-title":"The Gauss map of immersions of Riemannian manifolds in space of constant curvature","volume":"2","author":"Obata","year":"1968","journal-title":"J. Differ. Geom."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"407","DOI":"10.4134\/JKMS.2007.44.2.407","article-title":"Spherical submanifolds with finite type spherical Gauss map","volume":"44","author":"Chen","year":"2007","journal-title":"J. Korean Math. Soc."},{"doi-asserted-by":"crossref","unstructured":"Osserman, R. (1980). Minimal surfaces, Gauss maps, total curvature, eigenvalues estimates and stability. The Chern Symposium 1979, Springer.","key":"ref_29","DOI":"10.1007\/978-1-4613-8109-9_9"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1007\/s00025-016-0560-9","article-title":"Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map","volume":"71","author":"Bekts","year":"2017","journal-title":"Results Math."},{"doi-asserted-by":"crossref","unstructured":"Bekts, B., Canfes, E.O., and Dursun, U. (2017). Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map. Math. Nachrichten, 290.","key":"ref_31","DOI":"10.1002\/mana.201600498"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1515\/advgeom-2016-0005","article-title":"On spherical submanifolds with finite type spherical Gauss map","volume":"16","author":"Bekts","year":"2016","journal-title":"Adv. Geom."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1076\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:14:28Z","timestamp":1760188468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,27]]},"references-count":32,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["sym11091076"],"URL":"https:\/\/doi.org\/10.3390\/sym11091076","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,27]]}}}