The inverse Gudermannian in the hyperbolic geometry

2018/02/22 by Л. Н. Ромакина · 1 citation
Mathematics · Physics and Astronomy · #Mathematics and Applications #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Mathematics #Hyperbolic space #Inverse #Curvature #Mathematical analysis #Space (punctuation) #Metric (unit) #Cone (formal languages) #Hyperbolic triangle #Geometry #Integral geometry #Hyperbolic geometry #Pure mathematics #Differential geometry

paper · doi:10.1080/10652469.2018.1441296

openalex publication_date 2018/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/01/22

Abstract

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.

Cited by

• Gudermannian function [wikipedia]

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