Skip to main content
SpringerLink
Log in

On 3-Transitive Transformation Groups of the Lobachevskii Plane

  • Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. N. Sosov, “On the action of the multiplicative group of nonzero real numbers on the pointed Lobachevskii space,” Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 154 (4), 156–160 (2012).

    MathSciNet  Google Scholar 

  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 

  5. L. V. Sabinin, “Odules as a new approach to a geometry with a connection,” Sov. Math. Dokl. 233, 800–803 (1977).

    MathSciNet  MATH  Google Scholar 

  6. M. Hall, The Theory of Groups (Dover,Mineola, New York, 2018).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008, Russia

    L. I. Nigmatullina & E. N. Sosov

Authors
  1. L. I. Nigmatullina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. N. Sosov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. I. Nigmatullina.

Additional information

(Submitted by M. A. Malakhaltsev)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nigmatullina, L.I., Sosov, E.N. On 3-Transitive Transformation Groups of the Lobachevskii Plane. Lobachevskii J Math 39, 1403–1406 (2018). https://doi.org/10.1134/S1995080218090433

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080218090433

Keywords and phrases

Search

Navigation