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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. V. Aminova
AU  - D. R. Khakimov
TI  - Projective group properties of $h$-spaces of type $\{221\}$
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 87
EP  - 93
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_10_a8/
LA  - ru
ID  - IVM_2019_10_a8
ER  - 
%0 Journal Article
%A A. V. Aminova
%A D. R. Khakimov
%T Projective group properties of $h$-spaces of type $\{221\}$
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 87-93
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_10_a8/
%G ru
%F IVM_2019_10_a8
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/

[1] Aminova A. V., Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii, Yanus-K, M., 2003

[2] Aminova A. V., “Algebry Li infinitezimalnykh proektivnykh preobrazovanii lorentsevykh mnogoobrazii”, UMN, 50:1 (1995), 69–142 | Zbl

[3] Aminova A. V., Khakimov D. R., “O proektivnykh dvizheniyakh pyatimernykh prostranstv spetsialnogo vida”, Izv. vuzov. Matem., 2017, no. 5, 1–7

[4] Schur F., “Über den Zusammenhang der Räume konstanter Krümmungsmasses mit den projectiven Raumen”, Math. Ann., 27 (1886), 537–567 | MR