Geodesic
Finite closed 3(4)-loops of extended hyperbolic plane
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 14-26 
L. N. Romakina. Finite closed 3(4)-loops of extended hyperbolic plane. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 3, pp. 14-26. http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a1/
@article{ISU_2010_10_3_a1,
     author = {L. N. Romakina},
     title = {Finite closed 3(4)-loops of extended hyperbolic plane},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {14--26},
     year = {2010},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a1/}
}
TY  - JOUR
AU  - L. N. Romakina
TI  - Finite closed 3(4)-loops of extended hyperbolic plane
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2010
SP  - 14
EP  - 26
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a1/
LA  - ru
ID  - ISU_2010_10_3_a1
ER  - 
%0 Journal Article
%A L. N. Romakina
%T Finite closed 3(4)-loops of extended hyperbolic plane
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2010
%P 14-26
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/ISU_2010_10_3_a1/
%G ru
%F ISU_2010_10_3_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

This article considers finite closed $n$-loops of the extended hyperbolic plane $H^2$. 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.

[1] Rozenfeld B. A., Zamakhovskii M. P., Geometriya grupp Li. Simmetricheskie, parabolicheskie i periodicheskie prostranstva, MTsNMO, M., 2003, 560 pp. | MR

[2] Romakina L. N., Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, Nauchnaya kniga, Saratov, 2008, 279 pp.