Geodesic
Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. V. Lie algebras of projective and affine motions of $h$-spaces $H_{221}$ of type $\{221\}$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 12-28

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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 final part of the work. The first part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — 212. — P. 10–29. The second part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — xxx. — P. 10–37. The third part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — xxx. — P. 3–20. The fourth part: Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2022. — xxx. — P. 18–31.
Keywords: differential geometry, five-dimensional pseudo-Riemannian manifold, $h$-space, system of partial differential equations, nonhomothetical projective motion, Killing equation, projective Lie algebra. 
@article{INTO_2022_216_a1,
     author = {A. V. Aminova and D. R. Khakimov},
     title = {Lie algebras of projective motions of five-dimensional {pseudo-Riemannian} spaces. {V.} {Lie} algebras of projective and affine motions of $h$-spaces $H_{221}$ of type $\{221\}$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {12--28},
     publisher = {mathdoc},
     volume = {216},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_216_a1/}
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A. V. Aminova; D. R. Khakimov. Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. V. Lie algebras of projective and affine motions of $h$-spaces $H_{221}$ of type $\{221\}$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 12-28. http://geodesic.mathdoc.fr/item/INTO_2022_216_a1/