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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1403–1406 | Cite as

On 3-Transitive Transformation Groups of the Lobachevskii Plane

  • L. I. Nigmatullina
  • E. N. Sosov
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
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Abstract

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 phrases

Transformation group Lobachevskii plane Beltrami–Klein model Poincarémodel 3-transitivity 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lobachevskii Institute of Mathematics and MechanicsKazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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