Geodesic
Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. I. Preliminaries
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 10-29

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This work is devoted to the problem of studying multidimensional pseudo-Riemannian manifolds that admit Lie algebras of infinitesimal projective (in particular, affine) transformations, wider than Lie algebras of infinitesimal homotheties. Such manifolds have numerous geometric and physical applications. This paper is the first part of the work; continuation will be published in future issues.
Keywords: differential geometry, five-dimensional pseudo-Riemannian manifold, $h$-space, system of partial differential equations, nonhomothetical projective motion, Killing equation, projective Lie algebra. 
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A. V. Aminova; D. R. Khakimov. Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. I. Preliminaries. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 10-29. http://geodesic.mathdoc.fr/item/INTO_2022_212_a1/