On the holonomy of Lorentzian metrics. (English) Zbl 1213.53063

Boubel, Charles

Ann. Fac. Sci. Toulouse, Math. (6) 16, No. 3, 427-475 (2007).

Summary: Indecomposable Lorentzian holonomy algebras, except \(\mathfrak{so}(n,1)\) and \(\{0\}\), are not semi-simple; they possibly belong to four families of algebras. All four families are realized as families of holonomy algebras: we describe the corresponding set of germs of metrics in each case.

MSC:

53C29	Issues of holonomy in differential geometry
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

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