On 3-Transitive Transformation Groups of the Lobachevskii Plane
- Autores: Nigmatullina L.1, Sosov E.1
-
Afiliações:
- Lobachevskii Institute of Mathematics and Mechanics
- Edição: Volume 39, Nº 9 (2018)
- Páginas: 1403-1406
- Seção: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203452
- DOI: https://doi.org/10.1134/S1995080218090433
- ID: 203452
Citar
Resumo
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.
Palavras-chave
Sobre autores
L. Nigmatullina
Lobachevskii Institute of Mathematics and Mechanics
Autor responsável pela correspondência
Email: leysan.nigmatullina@bk.ru
Rússia, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008
E. Sosov
Lobachevskii Institute of Mathematics and Mechanics
Email: leysan.nigmatullina@bk.ru
Rússia, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008