Geodesic
Fan triangulations of a~hyperbolic plane of positive curvature
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 142-168.

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

We study the families $(\mathscr F_\lambda)$ of normal partitions of a $3$-$(1)$-contour $F$ of a hyperbolic plane $\widehat H$ of positive curvature into simple $4$-contours whose hyperbolic diagonal lines are parallel to the base of $F$. A $3$-$(1)$-contour with a given partition from a family $(\mathscr F_\lambda)$ (or some its normal subpartition) is called a fan. We construct fan partitions $\mathscr P_\text e$, $\mathscr P_\text h$ and $\mathscr P_\text p$ of $\widehat H$ whose symmetry groups are generated by a shift along an elliptic (respectively, hyperbolic and parabolic) straight line. It is proved that the partitions $\mathscr P_\text h$ and $\mathscr P_\text p$ are normal. The partitions $\mathscr P_\text h$ и $\mathscr P_\text p$ whose cells are trihedrals present examples of the first triangulations of $\widehat H$. 
@article{MT_2013_16_2_a8,
     author = {L. N. Romakina},
     title = {Fan triangulations of a~hyperbolic plane of positive curvature},
     journal = {Matemati\v{c}eskie trudy},
     pages = {142--168},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2013_16_2_a8/}
}
TY  - JOUR
AU  - L. N. Romakina
TI  - Fan triangulations of a~hyperbolic plane of positive curvature
JO  - Matematičeskie trudy
PY  - 2013
SP  - 142
EP  - 168
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2013_16_2_a8/
LA  - ru
ID  - MT_2013_16_2_a8
ER  - 
%0 Journal Article
%A L. N. Romakina
%T Fan triangulations of a~hyperbolic plane of positive curvature
%J Matematičeskie trudy
%D 2013
%P 142-168
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2013_16_2_a8/
%G ru
%F MT_2013_16_2_a8
L. N. Romakina. Fan triangulations of a~hyperbolic plane of positive curvature. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 142-168. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a8/

[1] Delone B. N., “Teoriya planigonov”, Izv. AN SSSR. Ser. matem., 23:3 (1959), 365–386 | MR | Zbl

[2] Rozenfeld B. A., Neevklidovy prostranstva, Nauka, M., 1969 | MR

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

[4] Romakina L. N., “Analog mozaiki na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Sb. nauch. tr. Mekhanika. Matematika, 12, no. 3, Izd-vo Sarat. un-ta, Saratov, 2010, 69–72

[5] Romakina L. N., “Konechnye zamknutye 3(4)-kontury rasshirennoi giperbolicheskoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 10:3 (2010), 14–26

[6] Romakina L. N., “Ovalnye linii giperbolicheskoi ploskosti polozhitelnoi krivizny”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:3 (2012), 37–44

[7] Romakina L. N., “Prostye razbieniya giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matem. sb., 203:9 (2012), 83–116 | DOI | MR | Zbl

[8] Romakina L. N., “Analogi formuly Lobachevskogo dlya ugla parallelnosti na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Sib. elektron. matem. izv., 10 (2013), 393–407

[9] Romakina L. N., Geometriya giperbolicheskoi ploskosti polozhitelnoi krivizny. Ch. 1: Trigonometriya, Izd-vo Sarat. un-ta, Saratov, 2013