Geodesic
Locally Conformally Homogeneous Pseudo-Riemannian Spaces
Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 130-168.

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

Locally homogeneous Riemannian spaces were studied in many papers. Locally conformally homogeneous Riemannian spaces were considered in [1]. Moreover, the theorem claiming that every such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space was proved. In this article, we study locally conformally homogeneous pseudo-Riemannian spaces and prove a theorem on their structure. Using three-dimensional Lie groups and the six-dimensional Heisenberg group [2], we construct some examples showing the difference between the Riemannian and pseudo-Riemannian cases for such spaces. 
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E. D. Rodionov; V. V. Slavskii; L. N. Chibrikova. Locally Conformally Homogeneous Pseudo-Riemannian Spaces. Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 130-168. http://geodesic.mathdoc.fr/item/MT_2006_9_1_a6/

[1] Alekseevskii D. V., “Odnorodnye rimanovy prostranstva otritsatelnoi krivizny”, Mat. sb., 96(138) (1975), 93–117 | MR | Zbl

[2] Besse A., Mnogoobraziya Einshteina, t. 1, 2, Mir, M., 1990 | MR | Zbl

[3] Gato M., Grosskhans F., Poluprostye algebry Li, Mir, M., 1981 | MR

[4] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya. Metody i prilozheniya, t. 1, Editorial URSS, M., 1998 | MR

[5] Reshetnik Yu. G., Teoremy ustoichivosti v geometrii i analize, Izd-vo In-ta matematiki RAN, Novosibirsk, 1996 | MR

[6] Rodionov E. D., Slavskii V. V., “Lokalno konformno odnorodnye prostranstva”, Dokl. RAN, 387:3 (2002), 314–317 | MR | Zbl

[7] Collinson S. D., “A comment on the integrability conditions of the conformal Killing equation”, Gen. Relativity Gravitation, 21:9 (1989), 979–980 | DOI | MR | Zbl

[8] Heber J., “Noncompact homogeneous Einstein Spaces”, Invent. Math., 133:2 (1998), 279–352 | DOI | MR | Zbl

[9] Milnor J., “Curvatures of left-invariant metrics on Lie groups”, Adv. Math., 21:3 (1976), 293–329 | DOI | MR | Zbl

[10] Rodionov E. D. and Slavskii V. V., “Conformal deformations of the Riemannian metrics and homogeneous Riemannian spaces”, Comment. Math. Univ. Carolin., 43:2 (2002), 271–282 | MR | Zbl

[11] Tricerri F. and Vanhecke L., Homogeneous Structures on Riemannian Manifolds, London Math. Soc. Lecture Note Ser., 83, Cambridge Univ. Press, Cambridge, etc., 1983 | MR | Zbl

[12] Yano K., The Theory of Lie Derivatives and Its Applications, North-Holland Publishing Co.; P. Noordhoff Ltd.; Interscience Publishers Inc., Amsterdam; Groningen; New York, 1957 | MR | Zbl