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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