Volume 5, Number 1,June 2002, Pages 11–15 ANALYTIC DEFINITIONS FOR HYPERBOLIC OBJECTS

Abstract. We can extend the hyperbolic space beyond the infinity and this extended space which contains hyperbolic space as a subset has many natural properties. The definitions for length, angle, and volume can be given by analytic continuation method. We also obtain theorems for the boundary regularity conditions of 2 and 3 dimensional region with finite volume. In [1] and [2] we considered an extended model of hyperbolic space and studied how we can define a volume of a region which lies beyond the infinity of the hyper-bolic space. Such investigation gives us a natural way of studying various geometric objects in Lorentz geometry in a manner consistent with those in hyperbolic ge