{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:11Z","timestamp":1760240651680,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T00:00:00Z","timestamp":1565913600000},"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":["2018R1D1A3B05050223"],"award-info":[{"award-number":["2018R1D1A3B05050223"]}],"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 the Euclidean space      E  n    , hyperplanes, hyperspheres and hypercylinders are the only isoparametric hypersurfaces. These hypersurfaces are also the only ones with chord property, that is, the chord connecting two points on them meets the hypersurfaces at the same angle at the two points. In this paper, we investigate hypersurfaces in nonflat space forms with the so-called geodesic chord property and classify such hypersurfaces completely.<\/jats:p>","DOI":"10.3390\/sym11081052","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T06:10:14Z","timestamp":1566195014000},"page":"1052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geodesic Chord Property and Hypersurfaces of Space Forms"],"prefix":"10.3390","volume":"11","author":[{"given":"Dong-Soo","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chonnam National University, Gwangju 61186, Korea"}]},{"given":"Young Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungpook National University, Daegu 41566, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8620-0676","authenticated-orcid":false,"given":"Dae Won","family":"Yoon","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,16]]},"reference":[{"key":"ref_1","unstructured":"Rademacher, H., and Toeplitz, O. (1994). The Enjoyment of Mathematics, Princeton Science Library, Princeton University Press. Translated from the Second (1933) German Edition and with Additional Chapters by H. Zuckerman."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"457","DOI":"10.5486\/PMD.2006.3450","article-title":"New characterization of W-curves","volume":"69","author":"Chen","year":"2006","journal-title":"Publ. Math. Debr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3002","DOI":"10.1016\/j.laa.2010.01.006","article-title":"New characterizations of spheres, cylinders and W-curves","volume":"432","author":"Kim","year":"2010","journal-title":"Linear Algebra Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/BF01420531","article-title":"A geometric characterization of the ball and the Bochner-Martinelli kernel","volume":"248","author":"Boas","year":"1980","journal-title":"Math. Ann."},{"key":"ref_5","first-page":"120","article-title":"Spheres and cylinders: A local geometric characterization","volume":"28","author":"Boas","year":"1984","journal-title":"Ill. J. Math."},{"key":"ref_6","first-page":"294","article-title":"A differential geometric proof of the local geometric characterization of spheres and cylinders by Boas","volume":"2","author":"Wegner","year":"1988","journal-title":"Math. Balk. (N.S.)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.laa.2014.12.014","article-title":"Ellipsoids and Elliptic hyperboloids in the Euclidean space En+1","volume":"471","author":"Kim","year":"2015","journal-title":"Linear Algebra Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.laa.2012.02.013","article-title":"Some characterizations of spheres and elliptic paraboloids","volume":"437","author":"Kim","year":"2012","journal-title":"Linear Algebra Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1016\/j.laa.2012.08.024","article-title":"Some characterizations of spheres and elliptic paraboloids II","volume":"438","author":"Kim","year":"2013","journal-title":"Linear Algebra Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.5831\/HMJ.2013.35.1.37","article-title":"A characterization of elliptic hyperboloids","volume":"35","author":"Kim","year":"2013","journal-title":"Honam Math. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1016\/j.crma.2014.09.003","article-title":"On standard imbeddings of hyperbolic spaces in the Minkowski space","volume":"352","author":"Kim","year":"2014","journal-title":"Comptes Rendus Math."},{"key":"ref_12","first-page":"509","article-title":"On the Gauss map of Hypersurfaces in the space form","volume":"32","author":"Kim","year":"1995","journal-title":"J. Korean Math. Soc."},{"key":"ref_13","unstructured":"K\u00fchnel, W. (2002). Differential Geometry, Curves-Surfaces-Manifolds, American Mathematical Society. Translated from the 1999 German Original by Bruce Hunt; Student Mathematical Library, 16."},{"key":"ref_14","unstructured":"O\u2019Neill, B. (1983). Semi-Riemannian Geometry with Applications to Relativity, Academic Press, Inc.. Pure and Applied Mathematics, 103."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:11:33Z","timestamp":1760188293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,16]]},"references-count":14,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["sym11081052"],"URL":"https:\/\/doi.org\/10.3390\/sym11081052","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,16]]}}}