The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 36-41.

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

We consider the first lacuna in the distribution of the mobility of n-dimensional (pseudo-)Riemannian spaces with respect to conformal mappings onto Einstein spaces. We obtain a tensor characteristic of spaces different from conformally flat ones, for which r=n1; this number is the maximal possible value. Thus, we have found maximally mobile spaces (different from conformally flat ones) with r=n1.
Mots-clés : mobility distribution, (pseudo-)Riemannian space, conformal mapping, Einstein space.
@article{IVM_2010_8_a3,
     author = {L. E. Evtushik and V. A. Kiosak and J. Mike\v{s}},
     title = {The mobility of {Riemannian} spaces with respect to conformal mappings onto {Einstein} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--41},
     publisher = {mathdoc},
     number = {8},
     year = {2010},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a3/}
}
TY  - JOUR
AU  - L. E. Evtushik
AU  - V. A. Kiosak
AU  - J. Mikeš
TI  - The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 36
EP  - 41
IS  - 8
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a3/
LA  - ru
ID  - IVM_2010_8_a3
ER  - 
%0 Journal Article
%A L. E. Evtushik
%A V. A. Kiosak
%A J. Mikeš
%T The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 36-41
%N 8
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a3/
%G ru
%F IVM_2010_8_a3
L. E. Evtushik; V. A. Kiosak; J. Mikeš. The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 36-41. https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a3/

[1] Eizenkhart L. P., Rimanova geometriya, In. lit., M., 1948

[2] Petrov A. Z., Novye metody v teorii otnositelnosti, Nauka, M., 1965

[3] Skhouten I. A., Stroik D. Dzh., Vvedenie v novye metody differentsialnoi geometrii, v. I, Gostekhizdat, M.–L., 1939

[4] Skhouten I. A., Stroik D. Dzh., Vvedenie v novye metody differentsialnoi geometrii, v. II, In. lit., M., 1949

[5] Denisov V. I., “Spetsialnye konformnye otobrazheniya v obschei teorii otnositelnosti”, Ukr. geometr. sb., 28, 1985, 43–50 | Zbl

[6] Brinkmann H. W., “Einstein spaces which mapped conformally on each other”, Math. Ann., 94 (1925), 117–145 | DOI | MR

[7] Mikesh I., Gavrilchenko M. L., Gladysheva E. I., “O konformnykh otobrazheniyakh na prostranstva Einshteina”, Vestn. Mosk. un-ta, 1994, no. 3, 13–17 | MR | Zbl

[8] Mikesh I., Gavrilchenko M. L., Gladysheva E. I., “O konformnykh otobrazheniyakh na prostranstva Einshteina”, Medunarodn. nauch. konf. “Lobachevskii i sovremennaya geometriya” (18–22 avgusta 1992), Tez. dokladov. Chast I, Izd-vo KGU, Kazan, 1992, 64

[9] Mikeš J., “Holomorphically projective mappings and their generalizations”, J. Math. Sci., 89:3 (1998), 1334–1353 | DOI | MR | Zbl

[10] Gover A. Rod, Nurowski P., “Obstructions to conformally Einstein metrics in $n$ dimensions”, J. Geom. Phys., 56:3 (2006), 450–484 | DOI | MR | Zbl