Geodesic Chord Property and Hypersurfaces of Space Forms
In the Euclidean space <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mi>n</mi> </msup> </semantics> </math> </inline-formula>,...
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MDPI AG
2019-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/1052 |
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doaj-1efa23cfe5764d2d817a9f669eb5207a2020-11-24T20:48:09ZengMDPI AGSymmetry2073-89942019-08-01118105210.3390/sym11081052sym11081052Geodesic Chord Property and Hypersurfaces of Space FormsDong-Soo Kim0Young Ho Kim1Dae Won Yoon2Department of Mathematics, Chonnam National University, Gwangju 61186, KoreaDepartment of Mathematics, Kyungpook National University, Daegu 41566, KoreaDepartment of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, KoreaIn the Euclidean space <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mi>n</mi> </msup> </semantics> </math> </inline-formula>, 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 <i>geodesic chord property</i> and classify such hypersurfaces completely.https://www.mdpi.com/2073-8994/11/8/1052geodesic chord propertyhyperspherehyperbolic spaceisoparametric hypersurface |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dong-Soo Kim Young Ho Kim Dae Won Yoon |
| spellingShingle |
Dong-Soo Kim Young Ho Kim Dae Won Yoon Geodesic Chord Property and Hypersurfaces of Space Forms Symmetry geodesic chord property hypersphere hyperbolic space isoparametric hypersurface |
| author_facet |
Dong-Soo Kim Young Ho Kim Dae Won Yoon |
| author_sort |
Dong-Soo Kim |
| title |
Geodesic Chord Property and Hypersurfaces of Space Forms |
| title_short |
Geodesic Chord Property and Hypersurfaces of Space Forms |
| title_full |
Geodesic Chord Property and Hypersurfaces of Space Forms |
| title_fullStr |
Geodesic Chord Property and Hypersurfaces of Space Forms |
| title_full_unstemmed |
Geodesic Chord Property and Hypersurfaces of Space Forms |
| title_sort |
geodesic chord property and hypersurfaces of space forms |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2019-08-01 |
| description |
In the Euclidean space <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mi>n</mi> </msup> </semantics> </math> </inline-formula>, 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 <i>geodesic chord property</i> and classify such hypersurfaces completely. |
| topic |
geodesic chord property hypersphere hyperbolic space isoparametric hypersurface |
| url |
https://www.mdpi.com/2073-8994/11/8/1052 |
| work_keys_str_mv |
AT dongsookim geodesicchordpropertyandhypersurfacesofspaceforms AT younghokim geodesicchordpropertyandhypersurfacesofspaceforms AT daewonyoon geodesicchordpropertyandhypersurfacesofspaceforms |
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1716808810013655040 |