{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:30:30Z","timestamp":1772253030829,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T00:00:00Z","timestamp":1539648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation","doi-asserted-by":"publisher","award":["2016R1A2B1006974"],"award-info":[{"award-number":["2016R1A2B1006974"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from the eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with a generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of G-type.<\/jats:p>","DOI":"10.3390\/sym10100514","type":"journal-article","created":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T11:07:51Z","timestamp":1539688071000},"page":"514","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces"],"prefix":"10.3390","volume":"10","author":[{"given":"Miekyung","family":"Choi","sequence":"first","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, 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":[[2018,10,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, B.-Y. 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Math."},{"key":"ref_10","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_11","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_12","first-page":"85","article-title":"Ruled surfaces with finite type Gauss map in Minkowski spaces","volume":"26","author":"Kim","year":"2006","journal-title":"Soochow J. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0393-0440(99)00063-7","article-title":"Ruled surfaces with pointwise 1-type Gauss map","volume":"34","author":"Kim","year":"2006","journal-title":"J. Geom. Phys."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","unstructured":"Yoon, D.W., Kim, D.-S., Kim, Y.H., and Lee, J.W. (2018). Hypersurfaces with generalized 1-type Gauss map. Mathematics, 6.","DOI":"10.3390\/math6080130"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/514\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:02Z","timestamp":1760196362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,16]]},"references-count":15,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["sym10100514"],"URL":"https:\/\/doi.org\/10.3390\/sym10100514","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201809.0407.v1","asserted-by":"object"}]},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,16]]}}}