On 3-Transitive Transformation Groups of the Lobachevskii Plane
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In this paper, we consider three transformation groups of the Lobachevskii plane that are generated by the group of all motions and one-parameter transformation groups, which preserve an elliptic, a hyperbolic or a parabolic bundle of straight lines of this plane, respectively. It is proved that each of these groups acts 3-transitively on the Lobachevskii plane. The transformation groups and their generalizations can be applied an research of quasi-conformal mappings of the Lobachevskii space, in the special theory of relativity and in the fractal geometry.
Keywords and phrasesTransformation group Lobachevskii plane Beltrami–Klein model Poincarémodel 3-transitivity
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- 2.E. N. Sosov, The Lobachevskii Geometry and its Application in the Special Theory of Relativity: Teaching Manual (Kazan Gos. Univ., Kazan, 2016) [in Russian].Google Scholar
- 3.Y. Y. Nut, The Geometry of Lobachevskii in the Analytic Presentation (Akad. Nauk SSSR,Moscow, 1961) [in Russian].Google Scholar
- 4.Y. L. Trainin, Analytical Geometry in Lobachevskii Space (Novosib. Gos. Ped. Inst., Novosibirsk, 1974) [in Russian].Google Scholar