The inverse Gudermannian in the hyperbolic geometry. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Romakina, L. N.
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 5(2018)
• Page Start: 384
• Page End: 401
• Publication Date: 2018-05-04
• Subjects: Hyperbolic space of positive curvature -- inverse Gudermannian -- angle of parallelism -- horocyclic polygon -- finite light cone -- volume; 51F05 -- 51F10 -- 51M25 -- 33E99; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1441296
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We present the first applications of the inverse Gudermannian in the geometry of the hyperbolic spaces of positive curvature. A hyperbolic spaceH ˆ n of positive curvature can be realised on the ideal domain of the Lobachevskii spaceΛ n . In this paper, the metric dependences for various figures of the planeH ˆ 2 are written down by the means of the inverse Gudermannian. The volume formula for a finite light cone of the spaceH ˆ 3 is obtained.