This article is cited in 12 papers

Locally Conformally Homogeneous Pseudo-Riemannian Spaces

E. D. Rodionov^a, V. V. Slavskii^b, L. N. Chibrikova<sup>a

a</sup> 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.

UDC: 514.765

Received: 18.07.2005

 English version: Siberian Advances in Mathematics, 2007, 17:3, 186–212

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