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

Présenté par : the Editorial Board

Kim, Dong-Soo1 ; Kim, Young Ho2 ; Yoon, Dae Won3
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, Tome 352 (2014) no. 12, pp. 1033-1038.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.003
Kim, Dong-Soo 1 ; Kim, Young Ho 2 ; Yoon, Dae Won 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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Kim, Dong-Soo; Kim, Young Ho; Yoon, Dae Won. On standard imbeddings of hyperbolic spaces in the Minkowski space. Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 1033-1038. doi : 10.1016/j.crma.2014.09.003. http://www.numdam.org/articles/10.1016/j.crma.2014.09.003/

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