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Boundary representations on the Lobachevsky plane
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Lobachevsky Geometry and Stellar Parallaxes
Siberian Mathematical Journal, 2022One aim of this paper is to provide proofs for the formulas and inequalities proposed without the proof by Lobachevsky in his first published paper on the subject of non-Euclidean geometry of 1829. These are obtained by computations in the Beltrami-Poincaré model.
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Lorentzian Geometry on the Lobachevsky Plane
Mathematical Notes, 2023The paper provides descriptions of length maximizing curves, distances, and spheres for left-invariant Lorentzian structures on connected simply connected non-abelian Lie groups of dimension \(2\). Using the Pontryagin maximum principle, the author gives these descriptions in terms of elementary functions.
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