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.
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