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Remarks on Lorentz symmetric spaces. (English) Zbl 1067.53009
The author considers homogeneous Lorentz spaces of dimension \(n \geq 3\). He proves that if such a space has “big” isotropy (that is, a non-precompact and irreducible isotropy group), then this space must have constant sectional curvature. This result provides a new direct proof of the fact that irreducible Lorentz symmetric spaces have constant curvature (this was known via algebraic classification).

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
22F30 Homogeneous spaces
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