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Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups. (English) Zbl 1126.53046
Čadek, Martin (ed.), The proceedings of the 25th winter school “Geometry and physics”, Srní, Czech Republic, January 15–22, 2006. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 79, 87-97 (2006).
In 1993, L. Bérard Bergery and A. Ikemakhen have classified weakly-irreducible not irreducible subalgebras of $${\mathbf{so}}(1,n+1)$$ [On the holonomy of Lorentzian manifolds, Proc. Symp. Pure Math. 54, 27–40 (1993; Zbl 0807.53014)]. In the present paper the author gives a geometrical proof of the above mentioned result. Transitively acting isometry groups of Lobachevskian spaces and transitively acting similarity transformation groups of Euclidean spaces are classified.
For the entire collection see [Zbl 1103.53001].

##### MSC:
 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C29 Issues of holonomy in differential geometry 58D19 Group actions and symmetry properties
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