Geodesic
Lie algebras of projective motions of five-dimensional $h$-spaces $H_{221}$ of type $\{221\}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 9-22

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We study five-dimensional pseudo-Riemannian $h$-spaces $H_{221}$ of type $\{221\}$. Necessary and sufficient conditions are determined under which $H_{221}$ is a space of constant (zero) curvature. Non-homothetical projective motions in $ H_{221} $ of non-constant curvature are found, homotheties and isometries of the indicated spaces are investigated. Dimensions, basic elements, and structure equations of maximal projective Lie algebras acting in $H_{221}$ of non-constant curvature are determined. As a result, the classification of $h$-spaces $H_{221}$ of type $\{221\}$ by (non-homothetical) Lie algebras of infinitesimal projective and affine transformations is obtained.
Keywords: five-dimensional pseudo-Riemannian manifold, $h$-space $H_ {221}$ of type $\{221\},$ non-homo-thetical projective motion, projective Lie algebra. 
@article{IVM_2021_12_a1,
     author = {A. V. Aminova and D. R. Khakimov},
     title = {Lie algebras of projective motions of five-dimensional $h$-spaces $H_{221}$ of type $\{221\}$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {9--22},
     publisher = {mathdoc},
     number = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a1/}
}
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A. V. Aminova; D. R. Khakimov. Lie algebras of projective motions of five-dimensional $h$-spaces $H_{221}$ of type $\{221\}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 9-22. http://geodesic.mathdoc.fr/item/IVM_2021_12_a1/