Geodesic
On projective motions of five-dimensional spaces of special form
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 97-102 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is devoted to the problem of determining of $5$-dimensional pseudo-Riemannian manifolds $ (M, g) $ admitting projective motions ($ h $-spaces). A similar problem for $ n $-dimensional proper Riemannian and Lorentz spaces was solved by Levi–Civita, Solodovnikov, Petrov and Aminova. For pseudo-Riemannian manifolds of arbitrary signature and dimension the problem of their classification in Lie algebras and Lie groups of projective transformations, set more than a hundred years ago, is still open. In this paper five-dimensional $ h $-spaces of the type $ \{221\} $ are determined using the method of skew-normal frame (Aminova) and necessary and sufficient conditions for the existence of projective motions of the same type are established.
Keywords: five-dimensional pseudo-Riemannian manifold, projective motion, $h$-space of the type $\{221\}$. 
@article{IVM_2017_5_a10,
     author = {A. V. Aminova and D. R. Khakimov},
     title = {On projective motions of five-dimensional spaces of special form},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {97--102},
     year = {2017},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_5_a10/}
}
TY  - JOUR
AU  - A. V. Aminova
AU  - D. R. Khakimov
TI  - On projective motions of five-dimensional spaces of special form
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 97
EP  - 102
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_5_a10/
LA  - ru
ID  - IVM_2017_5_a10
ER  - 
%0 Journal Article
%A A. V. Aminova
%A D. R. Khakimov
%T On projective motions of five-dimensional spaces of special form
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 97-102
%N 5
%U http://geodesic.mathdoc.fr/item/IVM_2017_5_a10/
%G ru
%F IVM_2017_5_a10
A. V. Aminova; D. R. Khakimov. On projective motions of five-dimensional spaces of special form. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 97-102. http://geodesic.mathdoc.fr/item/IVM_2017_5_a10/

[1] Levi-Civita T., “Sulle trasformazioni delle equazioni dinamiche”, Ann. di Mat., 24:2 (1896), 255–300 | DOI | Zbl

[2] Petrov A. Z., “O geodezicheskom otobrazhenii rimanovykh prostranstv neopredelennoi metriki”, Uchen. zap. Kazansk. un-ta, 109, no. 3, 1949, 7–36

[3] Solodovnikov A. S., “Proektivnye preobrazovaniya rimanovykh prostranstv”, UMN, 11:4 (1956), 45–116 | Zbl

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

[5] Aminova A. V., “Avtomorfizmy geometricheskikh struktur kak simmetrii differentsialnykh uravnenii”, Izv. vuzov. Matem., 1994, no. 2, 3–11 | MR

[6] Aminova A. V., “Proektivnye preobrazovaniya i simmetrii differentsialnykh uravnenii”, Matem. sb., 186:12 (1995), 21–37 | MR

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