Geodesic
Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. II. Integration of the Eisenhart equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 10-37

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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 second part of the work. The first part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — 212. — P. 10–29. 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. II. Integration of the Eisenhart equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 10-37. http://geodesic.mathdoc.fr/item/INTO_2022_213_a1/