{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:24:26Z","timestamp":1746804266089,"version":"3.40.5"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004085","name":"Ministry of Education, Science and Technology","doi-asserted-by":"publisher","award":["2012R1A1A2003994"],"award-info":[{"award-number":["2012R1A1A2003994"]}],"id":[{"id":"10.13039\/501100004085","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We study surfaces defined as graph of the function<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>z<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>in the product space<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msup><mml:mrow><mml:mi>\u210d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>\u00d7<\/mml:mo><mml:mi>\u211d<\/mml:mi><\/mml:math>. In particular, we completely classify flat or minimal surfaces given by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>+<\/mml:mo><mml:mi>v<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>v<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>are smooth functions.<\/jats:p>","DOI":"10.1155\/2014\/154294","type":"journal-article","created":{"date-parts":[[2014,3,26]],"date-time":"2014-03-26T03:11:17Z","timestamp":1395803477000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["Some Surfaces with Zero Curvature in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mi>\u210d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>\u00d7<\/mml:mo><mml:mi>\u211d<\/mml:mi><\/mml:math>"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8620-0676","authenticated-orcid":true,"given":"Dae Won","family":"Yoon","sequence":"first","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"4","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/19\/23\/102"},{"volume":"35","year":"1997","series-title":"Princeton Mathematical Series","key":"9"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2010.59.3983"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1353\/ajm.2007.0023"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972711003042"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1017\/S001708950400179X"},{"issue":"3","key":"7","first-page":"939","volume":"10","year":"2007","journal-title":"Bollettino della Unione Matematica Italiana B"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s005740200013"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.11650\/tjm.17.2013.2425"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2007.11.035"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/154294.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/154294.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/154294.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T08:38:02Z","timestamp":1469695082000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/154294\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":10,"alternative-id":["154294","154294"],"URL":"https:\/\/doi.org\/10.1155\/2014\/154294","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}