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

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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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     title = {Locally {Conformally} {Homogeneous} {Pseudo-Riemannian} {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/