Geodesic
On the properties of the projective Lie algebras of rigid $h$-spaces $H_{32}$ of the type $\{32\}$
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 2, pp. 111-119

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the $h$-space $H_{32}$ of non-constant curvature was found. Necessary and sufficient conditions were established for the existence of a non-homothetic projective motion in the $h$-space $H_{32}$ of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.
Keywords: five-dimensional pseudo-Riemannian manifold, rigid $h$-space of type $\{32\}$, Eisenhart equation, projective Lie algebra. 
@article{UZKU_2020_162_2_a0,
     author = {A. V. Aminova and D. R. Khakimov},
     title = {On the properties of the projective {Lie} algebras of rigid $h$-spaces $H_{32}$ of the type $\{32\}$},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {111--119},
     publisher = {mathdoc},
     volume = {162},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2020_162_2_a0/}
}
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A. V. Aminova; D. R. Khakimov. On the properties of the projective Lie algebras of rigid $h$-spaces $H_{32}$ of the type $\{32\}$. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 2, pp. 111-119. http://geodesic.mathdoc.fr/item/UZKU_2020_162_2_a0/