Geodesic Chord Property and Hypersurfaces of Space Forms
Department of Mathematics, Chonnam National University, Gwangju 61186, Korea
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1052; https://doi.org/10.3390/sym11081052 (registering DOI)
Received: 22 July 2019 / Revised: 13 August 2019 / Accepted: 14 August 2019 / Published: 16 August 2019
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In the Euclidean space
, 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.
This is an open access article distributed under the Creative Commons Attribution License
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MDPI and ACS Style
Kim, D.-S.; Kim, Y.H.; Yoon, D.W. Geodesic Chord Property and Hypersurfaces of Space Forms. Symmetry 2019, 11, 1052.
Kim D-S, Kim YH, Yoon DW. Geodesic Chord Property and Hypersurfaces of Space Forms. Symmetry. 2019; 11(8):1052.
Kim, Dong-Soo; Kim, Young H.; Yoon, Dae W. 2019. "Geodesic Chord Property and Hypersurfaces of Space Forms." Symmetry 11, no. 8: 1052.
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