Geodesic
On the action of the multiplicative group of nonzero real numbers on the pointed Lobachevsky space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 156-160 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider the pointed Lobachevsky space $\Lambda$. In terms of the Beltrami–Klein model, we obtain an explicit expression for the action of the multiplicative group of nonzero real numbers on the space $\Lambda$. This action is analogous to that of this group on the pointed Euclidean space.
Keywords: Lobachevsky space, Beltrami–Klein model, multiplicative group of nonzero real numbers. 
@article{UZKU_2012_154_4_a13,
     author = {E. N. Sosov},
     title = {On the action of the multiplicative group of nonzero real numbers on the pointed {Lobachevsky} space},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {156--160},
     year = {2012},
     volume = {154},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a13/}
}
TY  - JOUR
AU  - E. N. Sosov
TI  - On the action of the multiplicative group of nonzero real numbers on the pointed Lobachevsky space
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2012
SP  - 156
EP  - 160
VL  - 154
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a13/
LA  - ru
ID  - UZKU_2012_154_4_a13
ER  - 
%0 Journal Article
%A E. N. Sosov
%T On the action of the multiplicative group of nonzero real numbers on the pointed Lobachevsky space
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2012
%P 156-160
%V 154
%N 4
%U http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a13/
%G ru
%F UZKU_2012_154_4_a13
E. N. Sosov. On the action of the multiplicative group of nonzero real numbers on the pointed Lobachevsky space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 156-160. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a13/

[1] Shirokov P. A., Kratkii ocherk osnov geometrii Lobachevskogo, Nauka, M., 1983, 80 pp. | MR

[2] Nut Yu. Yu., Geometriya Lobachevskogo v analiticheskom izlozhenii, Izd-vo AN SSSR, M., 1961, 311 pp. | MR

[3] Sosov E. N., Geometriya Lobachevskogo i eë primenenie v spetsialnoi teorii otnositelnosti. Chast 1. Geometriya Lobachevskogo, Kazan. un-t, Kazan, 2012, 38 pp.

[4] Sabinin L. V., “Oduli kak novyi podkhod k geometrii so svyaznostyu”, Dokl. AN SSSR, 233:5 (1977), 800–803 | MR | Zbl

[5] Sosov E. N., “Ob odnom odule v geometrii Gilberta”, Izv. vuzov. Matem., 1995, no. 5, 78–82 | MR | Zbl

[6] Sosov E. N., Geometries of convex and finite sets of geodesic spaces, 2010, 256 pp., arXiv: 1011.6191v1[math.MG]

[7] Sabinin L. V., Mikheev P. O., “O zakone slozheniya skorostei v spetsialnoi teorii otnositelnosti”, Usp. matem. nauk, 48:5(293) (1993), 183–184 | MR | Zbl

[8] Sosov E. N., Geometriya Lobachevskogo i eë primenenie v spetsialnoi teorii otnositelnosti. Chast 2. Primenenie geometrii Lobachevskogo v spetsialnoi teorii otnositelnosti, Kazan. un-t, Kazan, 2012, 32 pp.

[9] Matveev O. A., Nesterenko E. L., Universalnye algebry v teorii prostranstv affinnoi svyaznosti, blizkikh k simmetricheskim, Izd-vo MGOU, M., 2012, 132 pp.