Geodesic
Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces.~II
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2014), pp. 33-47.

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

This paper describes all invariant affine connections on three-dimensional pseudo-Riemannian homogeneous spaces of dimension 3. We present complete local classification of pseudo-Riemannian homogeneous spaces. It is equivalent to the description of effective pairs of Lie algebras supplied with an invariant nondegenerate symmetric bilinear form on the isotropy module. We describe all invariant affine connections on pseudo-Riemannian homogeneous spaces together with their curvature and torsion tensors, and choose pseudo-Riemannian connections.
Mots-clés : invariant affine connection
Keywords: pseudo-Riemannian homogeneous spaces. 
@article{IVM_2014_6_a3,
     author = {N. P. Mozhey},
     title = {Affine connections on three-dimensional {pseudo-Riemannian} homogeneous {spaces.~II}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--47},
     publisher = {mathdoc},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_6_a3/}
}
TY  - JOUR
AU  - N. P. Mozhey
TI  - Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces.~II
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 33
EP  - 47
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_6_a3/
LA  - ru
ID  - IVM_2014_6_a3
ER  - 
%0 Journal Article
%A N. P. Mozhey
%T Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces.~II
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 33-47
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_6_a3/
%G ru
%F IVM_2014_6_a3
N. P. Mozhey. Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces.~II. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2014), pp. 33-47. http://geodesic.mathdoc.fr/item/IVM_2014_6_a3/

[1] Mozhei N. P., “Affinnye svyaznosti na trekhmernykh psevdorimanovykh odnorodnykh prostranstvakh. I”, Izv. vuzov. Matem., 2013, no. 12, 51–68

[2] Levi-Civita T., “Nozione di parallelismo in una varietà qualunque”, Rend. Circ. Mat. Palermo, 42 (1917), 173–205 | DOI

[3] Weyl H., Raum, Zeit, Materie, Springer, 1970 | MR | Zbl

[4] Lumiste Yu. G., “Teoriya svyaznostei v rassloennykh prostranstvakh”, Itogi nauki i tekhn. Algebra. Topologiya. Geometriya. 1969, VINITI AN SSSR, M., 1971, 123–168 | MR | Zbl

[5] Kruchkovich G. I., “Klassifikatsiya trekhmernykh rimanovykh prostranstv po gruppam dvizhenii”, UMN, 9:1 (1954), 3–40 | MR | Zbl

[6] Thurston W., “Three-dimensional manifolds, Kleinian groups and hyperbolic geometry”, Bull. Amer. Math. Soc., 6 (1982), 357–381 | DOI | MR

[7] Scott P., “The geometries of 3-manifolds”, Bull. London Math. Soc., 15:5 (1983), 401–487 | DOI | MR | Zbl

[8] Kobayashi S., Nomizu K., Foundations of differential geometry, v. I, N.Y.–London, 1963 ; v. II, N.Y.–London, 1969 | MR

[9] Komrakov B., Tchourioumov A., Mozhey N. et al., Three-dimensional isotropically-faithful homogeneous spaces, Preprints No 35–37, Univ. Oslo, 1993

[10] Nomizu K., “Invariant affine connections on homogeneous spaces”, Amer. J. Math., 76:1 (1954), 33–65 | DOI | MR | Zbl

[11] Kowalski O., “Riemannian manifolds with homogeneous geodesics”, Boll. Unione Math. Ital. VII. Ser. B, 5:1 (1991), 189–246 | MR | Zbl