Asymptotic lines on pseudospheres and the angle of parallelism

DOI10.3103/S1066369X21060037zbMath1471.53010OpenAlexW3178520782MaRDI QIDQ2041624

A. V. Kostin

Publication date: 23 July 2021

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x21060037

zbMATH Keywords

Minkowski spacepseudospherede Sitter planeasymptotic lineLobachevsky plane

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) PDEs in connection with relativity and gravitational theory (35Q75) Local submanifolds (53B25) Non-Euclidean differential geometry (53A35)

Cites Work

• \(C^ \infty\)-isometric imbeddings of the hyperbolic plane and of cylinders with hyperbolic metric in spherical spaces
• Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature
• Analytical approaches to the study of the sine-Gordon equation and pseudospherical surfaces
• Interpretation of geometry on manifolds as a geometry in a space with projective metric
• Geometrical interpretation of the sinh-Gordon equation
• Möbius structures and timed causal spaces on the circle
• Asymptotic Lines on the Pseudo-Spherical Surfaces
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