{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T22:48:19Z","timestamp":1770331699234,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,12]],"date-time":"2018-09-12T00:00:00Z","timestamp":1536710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space     E 4    . We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace\u2013Beltrami operator. Moreover, we calculate the third Laplace\u2013Beltrami operator of the rotational hypersurface in      E 4  .     We also draw some figures of the rotational hypersurface.<\/jats:p>","DOI":"10.3390\/sym10090398","type":"journal-article","created":{"date-parts":[[2018,9,12]],"date-time":"2018-09-12T10:26:36Z","timestamp":1536747996000},"page":"398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3264-6239","authenticated-orcid":false,"given":"Erhan","family":"G\u00fcler","sequence":"first","affiliation":[{"name":"Faculty of Sciences, Department of Mathematics, Bart\u0131n University, Bart\u0131n 74100, Turkey"}]},{"given":"Hasan Hilmi","family":"Hac\u0131saliho\u011flu","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, Department of Mathematics, \u015eeyh Edebali University (Emeritus), Bilecik 11230, Turkey"}]},{"given":"Young Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"353","DOI":"10.4064\/cm-72-2-353-361","article-title":"On Weyl pseudosymmetric hypersurfaces","volume":"72","author":"Arslan","year":"1997","journal-title":"Colloq. 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