Remarks on Lorentz symmetric spaces. (English) Zbl 1067.53009

Zeghib, Abdelghani

Compos. Math. 140, No. 6, 1675-1678 (2004).

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).

Reviewer: Vladislav V. Goldberg (Livingston)

MSC:

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

Keywords:

Lorentz; isotropy; constant curvature; constant sectional curvature; symmetric space