The inverse Gudermannian in the hyperbolic geometryстатья
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Аннотация:We present the first applications of the inverse Gudermannian in the geometry of the hyperbolic spaces of positive curvature. A hyperbolic space Hˆn of positive curvature can be realised on the ideal domain of the Lobachevskii space Λn. In this paper, the metric dependences for various figures of the plane Hˆ2 are written down by the means of the inverse Gudermannian. The volume formula for a finite light cone of the space Hˆ3 is obtained.
KEYWORDS: Hyperbolic space of positive curvature, inverse Gudermannian, angle of parallelism, horocyclic polygon, finite light cone, volume
CLASSIFICATIONS: 51F05, 51F10, 51M25, 33E99