Geodesic
Structure of the projective group in a pseudo-Riemannian space
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 30-41 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study $n$-dimensional pseudo-Riemannian spaces $V^n(g_{ij})$ with an arbitrary signature that admit projective motions, i.e., groups of continuous transformations preserving geodesics. In particular, we find the metric of a pseudo-Riemannian space of special type and establish important projective-group properties of this space.
Keywords: differential geometry, general relativity theory, pseudo-Riemannian manifold, systems of partial differential equations. 
@article{TMF_2018_196_1_a2,
     author = {Z. Kh. Zakirova},
     title = {Structure of the~projective group in {a~pseudo-Riemannian} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {30--41},
     year = {2018},
     volume = {196},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a2/}
}
TY  - JOUR
AU  - Z. Kh. Zakirova
TI  - Structure of the projective group in a pseudo-Riemannian space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 30
EP  - 41
VL  - 196
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a2/
LA  - ru
ID  - TMF_2018_196_1_a2
ER  - 
%0 Journal Article
%A Z. Kh. Zakirova
%T Structure of the projective group in a pseudo-Riemannian space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 30-41
%V 196
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a2/
%G ru
%F TMF_2018_196_1_a2
Z. Kh. Zakirova. Structure of the projective group in a pseudo-Riemannian space. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 30-41. http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a2/

[1] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya, URSS, M., 1998 | MR

[2] L. P. Eizenkhart, Rimanova geometriya, IL, M., 1948 | MR | Zbl

[3] G. Konigs, “Appl. II”: G. Darboux, Leçons sur la théorie généralle des surfaces. IV, Gauthier-Villars, Paris, 1896, 368–404 | MR

[4] A. Z. Petrov, “O geodezicheskom otobrazhenii rimanovykh prostranstv neopredelennoi metriki”, Uch. zap. Kazan. un-ta, 109:3 (1949), 7–36

[5] G. Fubini, “Sui gruppi transformazioni geodetiche”, Mem. Acc. Torino. Cl. Fif. Mat. Nat., 53 (1903), 261–313 | Zbl

[6] A. S. Solodovnikov, “Proektivnye preobrazovaniya rimanovykh prostranstv”, UMN, 11:4(70) (1956), 45–116 | MR | Zbl

[7] A. V. Aminova, “Algebry Li infinitezimalnykh proektivnykh preobrazovanii lorentsevykh mnogoobrazii”, UMN, 50:1(301) (1995), 69–142 | DOI | MR | Zbl

[8] Z. Kh. Zakirova, Proektivno-gruppovye svoistva $6$-mernykh teorii tipa Kalutsy–Kleina, Diss. ... kand. fiz.-matem. nauk, KGU, Kazan, 2001

[9] Z. Kh. Zakirova, “Pervye integraly uravnenii geodezicheskikh $h$-prostranstv tipa $[51]$”, Mezhvuz. temat. sb. nauch. tr., Trudy geometricheskogo seminara, 23, Izd-vo Kazan. matem. obsch-va, Kazan, 1997, 57–64 | MR

[10] Z. Kh. Zakirova, “Pervye integraly uravnenii geodezicheskikh h-prostranstv tipa $[411]$”, Izv. vuzov. Matem., 1999, no. 9, 78–79 | MR | Zbl

[11] Z. Kh. Zakirova, “Zhestkie shestimernye $h$-prostranstva postoyannoi krivizny”, TMF, 158:3 (2009), 347–354 | DOI | DOI | MR | Zbl

[12] Z. Kh. Zakirova, “Metriki 6-mernykh h-prostranstv tipov $[3(21)]$, $[(32)1]$, $[(321)]$”, Kratkie soobscheniya po fizike FIAN, 38:9 (2011), 270–274

[13] Z. Kh. Zakirova, “O nekotorykh spetsialnykh resheniyakh uravneniya Eizenkharta”, Ufimskii matem. zhurn., 5:3 (2013), 41–53 | DOI