Nous établissons quelques caractérisations des plongements standard d'espaces hyperboliques dans l'espace de Minkowski de dimension , avec des propriétés intrinsèques et extrinsèques comme la surface n-dimensionnelle des sections coupées par des hyperplans, le volume en 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 de dimension .
We establish some characterizations of the standard imbeddings of hyperbolic spaces in the -dimensional Minkowski space with intrinsic and extrinsic properties such as the n-dimensional area of the sections cut off by hyperplanes, the -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 -dimensional Euclidean space .
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Dong-Soo Kim 1 ; Young Ho Kim 2 ; Dae Won Yoon 3
@article{CRMATH_2014__352_12_1033_0, author = {Dong-Soo Kim and Young Ho Kim and Dae Won Yoon}, title = {On standard imbeddings of hyperbolic spaces in the {Minkowski} space}, journal = {Comptes Rendus. Math\'ematique}, pages = {1033--1038}, publisher = {Elsevier}, volume = {352}, number = {12}, year = {2014}, doi = {10.1016/j.crma.2014.09.003}, language = {en}, }
TY - JOUR AU - Dong-Soo Kim AU - Young Ho Kim AU - Dae Won Yoon TI - On standard imbeddings of hyperbolic spaces in the Minkowski space JO - Comptes Rendus. Mathématique PY - 2014 SP - 1033 EP - 1038 VL - 352 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2014.09.003 LA - en ID - CRMATH_2014__352_12_1033_0 ER -
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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