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This article is cited in 12 scientific papers (total in 12 papers)
Locally Conformally Homogeneous Pseudo-Riemannian Spaces
E. D. Rodionova, V. V. Slavskiib, L. N. Chibrikovaa a Barnaul State Pedagogical University
b Ugra Research Institute of Information Technologies
Abstract:
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.
Key words:
conformal deformations, (pseudo-)Riemannian metric, homogeneous spaces.
Received: 18.07.2005
Citation:
E. D. Rodionov, V. V. Slavskii, L. N. Chibrikova, “Locally Conformally Homogeneous Pseudo-Riemannian Spaces”, Mat. Tr., 9:1 (2006), 130–168; Siberian Adv. Math., 17:3 (2007), 186–212
Linking options:
https://www.mathnet.ru/eng/mt42 https://www.mathnet.ru/eng/mt/v9/i1/p130
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Abstract page: | 502 | Full-text PDF : | 186 | References: | 64 | First page: | 1 |
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