Some applications of the Lorentzian holonomy algebras. (English) Zbl 1261.53048

Galaev, Anton

J. Geom. Symmetry Phys. 26, 13-31 (2012).

Summary: It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds with given recurrent curvature tensor, and the classification of two-symmetric Lorentzian manifolds is explained. Then the conformally recurrent Lorentzian manifolds are classified and the recurrent symmetric bilinear forms on these manifolds are described.

MSC:

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

Keywords:

holonomy algebras; recurrent curvature tensor; recurrent symmetric bilinear forms; Lorentzian symmetric spaces