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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; (registering DOI)
Received: 22 July 2019 / Revised: 13 August 2019 / Accepted: 14 August 2019 / Published: 16 August 2019
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
PDF [233 KB, uploaded 16 August 2019]


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. View Full-Text
Keywords: geodesic chord property; hypersphere; hyperbolic space; isoparametric hypersurface geodesic chord property; hypersphere; hyperbolic space; isoparametric hypersurface
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kim, D.-S.; Kim, Y.H.; Yoon, D.W. Geodesic Chord Property and Hypersurfaces of Space Forms. Symmetry 2019, 11, 1052.

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