Document Zbl 1111.53020

Screen bundles of Lorentzian manifolds and some generalisations of \(pp\)-waves. (English) Zbl 1111.53020

J. Geom. Phys. 56, No. 10, 2117-2134 (2006).

The paper studies Lorentzian manifolds \((M,g)\) which admit a recurrent light-like vector field \(X\). If Riem\((U,V)\) maps \(RX\) into \((RX)^\perp\) for all vectors \(U,V\) then \((M,g)\) is called a \(pr\)-wave spacetime. Here Riem denotes the Riemann curvature tensor. If Riem\( (U,V)\) maps \((RX)^\perp\) into \(RX\) then \((M,g)\) is said to have light-like hypersurface curvature. Both the new types generalize the well-known \(pp\)-wave spacetimes. The author derives alternative characterizations by holonomy properties and in terms of adapted coordinates.

Reviewer: Rainer Schimming (Greifswald)

Cited in 17 Documents

MSC:

53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53C29	Issues of holonomy in differential geometry
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Keywords:

\(pr\)-wave

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References:

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