2023 №54(2)

Bianchi transformation of the pseudosphere

DOI

10.5922/0321-4796-2023-54-2-7

Pages

71-77

Abstract

The work is devoted to the study of the Bianchi transform for surfa­ces of constant negative Gaussian curvature. The surfaces of rotation of cons­tant negative Gaussian curvature are the Minding top, the Minding coil, the pseudosphere (Beltrami surface). Surfaces of constant negative Gaus­sian curvature also include Kuens surface and the Dinis surface. The study of surfaces of constant negative Gaussian curvature (pseudosphe­ri­cal surfaces) is of great importance for the interpretation of Lobachevsky planimetry. The connection of the geometric characteristics of pseudos­phe­rical surfaces with the theory of networks, with the theory of solitons, with nonlinear differential equations and sin-Gordon equations is estab­li­shed. The sin-Gordon equation plays an important role in modern physics. Bianchi transformations make it possible to obtain new pseudospherical surfaces from a given pseudospherical surface. The Bianchi transform for the pseudosphere is constructed. Using a mathematical package, the pseu­dos­phere and its Bianchi transform are constructed.

Reference

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