On standard imbeddings of hyperbolic spaces in the Minkowski space

Abstract

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. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.