Cite this article as:

Romakina L. N. Finite Closed 3(4)-Loops of Extended Hyperbolic Plane. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2010, vol. 10, iss. 3, pp. 14-26. DOI: https://doi.org/10.18500/1816-9791-2010-10-3-14-26

Language: 
Russian
Heading: 
Mathematics
UDC: 
514.133+514.1

Finite Closed 3(4)-Loops of Extended Hyperbolic Plane

Authors: 
Romakina Lyudmila Nikolaevna, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , romakinaln@mail.ru
Abstract: 

This article considers finite closed n-loops of the extended hyperbolic plane H2. The paper deals with topological and metric properties of the finite closed 3(4)-loops. Pasha statement analogues have been also obtained. We proved the existence of two types 4-loops and convexity of the plain 4-loop.

Key words: 
finite closed n-loop, plain 4-loop, interior of a finite closed isotropic loop, convex finite closed loop
DOI: 
https://doi.org/10.18500/1816-9791-2010-10-3-14-26
References

1. Розенфельд, Б.А. Геометрия групп Ли. Симметрические, параболические и периодические пространства / Б.А. Розенфельд, М.П. Замаховский. – М.: МЦНМО, 2003. – 560 с.
2. Ромакина, Л.Н. Геометрии коевклидовой и копсевдоевклидовой плоскостей / Л.Н. Ромакина. – Саратов: Научная книга, 2008. – 279 с.
 

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