Examples of indecomposable non-irreducible Lorentzian manifolds. (English. Extended French summary) Zbl 0873.53009

Ikemakhen, A.

Ann. Sci. Math. Qué. 20, No. 1, 53-66 (1996).

The author considers holonomy groups of indecomposable non-irreducible Lorentzian manifolds. He constructs a coordinate system in which he obtains a reduced form of the metric of such a manifold. Moreover, he describes some particular cases when there is further information about the restricted holonomy group of the metric. Finally, he shows that an Einstein Lorentzian manifold can be neither of type 3 nor of type 4.

Reviewer: M.Hotloś (Wrocław)

MSC:

53B30

Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

non-irreducible manifolds; indecomposable manifolds; Einstein manifold; holonomy groups