Conformally flat Lorentzian manifolds with special holonomy

Details Conformally flat Lorentzian manifolds with special holonomy Conformally flat Lorentzian manifolds with special holonomy

2010-11-17

arxiv.org/abs/1011.3977v2

Mathematics

Differential Geometry

two new classes of metrics are found; 18 pages

Scientific paper

It is shown that among conformally flat Lorentzian manifolds there are four
classes of spaces with special holonomy groups: pp-waves with a certain
potential and three classes of spaces with the holonomy group $\Sim(n)$, which
can be described as extensions of Riemannian spaces of constant sectional
curvature to certain Walker metrics.

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