Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Romakina L. N. Finite Closed 5-Loops of Extended Hyperbolic Plane. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 1, pp. 38-49. DOI: 10.18500/1816-9791-2011-11-1-38-49

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.01.2011
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Russian
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UDC: 
514.133+514.17

Finite Closed 5-Loops of Extended Hyperbolic Plane

Autors: 
Romakina Lyudmila Nikolaevna, Saratov State University
Abstract: 

There are four types of finite closed 5-loops which are invariant by the fundamental group G and singled out on the extended hyperbolic plane H2. It is proved that convex 5-loops belong to two types. The interior of the first type 5-loop coincides with the plane H2 . The 5-loop of the second type allows the partition into two simple loops of three and four dimension. Its interior coincides with the interior of the component of the simple 4-loop. The topological 5-loop properties are researched.

References: 
  1. Ромакина, Л.Н. Конечные замкнутые 3(4)- контуры расширенной гиперболической плоскости / Л.Н. Ромакина // Изв. Сарат. ун-та. Нов. сер. 2010. Т. 10. Сер. Математика. Механика. Информатика, вып. 3. С. 14–26.
  2. Ромакина, Л.Н. Геометрии коевклидовой и копсевдоевклидовой плоскостей / Л.Н. Ромакина. Саратов: Науч. книга, 2008.