Geodesic
$h$-spaces of type $\{2,2,1\}$ having constant curvature
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 65-71
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In order to find projective transformations of a pseudo-Riemannian manifold one can use A. V. Aminov's method of skew-orthogonal frame [1]. This method makes it possible to reduce the problem to solving Eisenhart equations and generalized Killing equations. In the present paper we integrate the Eisenhart equations for 5-dimensional $h$-spaces of type $\{2,1,1\}$. 
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A. N. Karuzin. $h$-spaces of type $\{2,2,1\}$ having constant curvature. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 65-71. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a7/

[1] Aminova A. V., Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii, Yanus-K, M., 2003, 619 pp.

[2] Solodovnikov A. S., “Proektivnye preobrazovaniya rimanovykh prostranstv”, UMN, 1956, no. 11, 45–116 | MR | Zbl

[3] Eizenkhart L. P., Rimanova geometriya, Inostr. lit-ra, M., 1948