Geodesic
Projective group properties of $h$-spaces of type $\{221\}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 87-93

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We investigate the curvature of a 5-dimensional $h$-space $H_{221} $ of the type $\{221\}$ [3], necessary and sufficient conditions are obtained in order that $ H_ {221} $ be a space of constant curvature $K$ (theorem 1). A general solution of the Eisenhart equation is found in the $h$-space $H_ {221}$ of non-constant curvature. The necessary and sufficient conditions for the existence of non-homothetical projective motion in the $h$-space $ H_{221} $ of non-constant curvature are established (theorem 5) and, as a consequence, the structure of the non-homothetical projective Lie algebra in such a space is determined (theorem 6).
Keywords: five-dimensional pseudo-Riemannian manifold, the Eisenhart equation, projective Lie algebra, $h$-space of the type $\{221 \}$. 
@article{IVM_2019_10_a8,
     author = {A. V. Aminova and D. R. Khakimov},
     title = {Projective group properties of $h$-spaces of type $\{221\}$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {87--93},
     publisher = {mathdoc},
     number = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_10_a8/}
}
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A. V. Aminova; D. R. Khakimov. Projective group properties of $h$-spaces of type $\{221\}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 87-93. http://geodesic.mathdoc.fr/item/IVM_2019_10_a8/