Comptes Rendus
no. 12
Geometry/Differential geometry
On standard imbeddings of hyperbolic spaces in the Minkowski space

Presented by: the Editorial Board

Dong-Soo Kim1; Young Ho Kim2; Dae Won Yoon3
1 Department of Mathematics, Chonnam National University, Gwangju 500-757, South Korea
2 Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
3 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, South Korea
Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1033-1038.

We establish some characterizations of the standard imbeddings of hyperbolic spaces in the (n+1)-dimensional Minkowski space Ln+1 with intrinsic and extrinsic properties such as the n-dimensional area of the sections cut off by hyperplanes, the (n+1)-dimensional volume of regions between parallel hyperplanes, and the n-dimensional surface area of regions between parallel hyperplanes. In the same manner, we give an affirmatively partial answer to Question A suggested in [6], which is for the characterization of hyperspheres in the (n+1)-dimensional Euclidean space En+1.

Nous établissons quelques caractérisations des plongements standard d'espaces hyperboliques dans l'espace de Minkowski Ln+1 de dimension n+1, avec des propriétés intrinsèques et extrinsèques comme la surface n-dimensionnelle des sections coupées par des hyperplans, le volume en n+1 dimensions de régions entre des hyperplans parallèles et la surface n-dimensionnelle de régions entre des hyperplans parallèles. De la même façon, nous donnons une réponse affirmative partielle à la question A suggérée dans [6], qui concerne la caractérisation d'hypersphères dans l'espace Euclidien En+1 de dimension n+1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.09.003

Dong-Soo Kim 1; Young Ho Kim 2; Dae Won Yoon 3

1 Department of Mathematics, Chonnam National University, Gwangju 500-757, South Korea
2 Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
3 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, South Korea 
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Dong-Soo Kim; Young Ho Kim; Dae Won Yoon. On standard imbeddings of hyperbolic spaces in the Minkowski space. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1033-1038. doi : 10.1016/j.crma.2014.09.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.003/

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