Geodesic
Two-dimensional pseudo-Riemannian metrics reconstructed by a given curvature
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 85-92 
È. R. Rozendorn; D. D. Sokolov. Two-dimensional pseudo-Riemannian metrics reconstructed by a given curvature. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 85-92. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a2/
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     title = {Two-dimensional {pseudo-Riemannian} metrics reconstructed by a~given curvature},
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     pages = {85--92},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of reconstruction of a two-dimensional, pseudo-Riemannian metric in isotropic coordinates by a given Gaussian curvature is considered. In particular, we present sufficient conditions for the possibility of reconstruction such a metric in a coordinate quadrant. Possible applications of results obtained are discussed.

[1] Artykbaev A., Sokolov D. D., Geometriya v tselom v ploskom prostranstve-vremeni, Fan, Tashkent, 1991 | Zbl

[2] Lamburt V. G., Rozendorn E. R., Sokolov D. D., Tutubalin V. N., “Geodezicheskie so sluchainoi kriviznoi na rimanovykh i psevdorimanovykh mnogoobraziyakh”, Trudy geometr. seminara, 24, KGU, Kazan, 2003, 99–106

[3] Penrouz R., Struktura prostranstva-vremeni, Merkurii, Cherepovets, 2000

[4] Pogorelov A. V., Lektsii po differentsialnoi geometrii, KhGU, Kharkov, 1967

[5] Poznyak E. G., “Geometricheskie issledovaniya, svyazannye s uravneniem $z_{xy}=\sin z$”, Itogi nauki i tekhn. Ser. Probl. geom., 8, 1977, 225–241 | MR | Zbl

[6] Uizem Dzh., Lineinye i nelineinye volny, Nauka, M., 1977