Pseudo-Riemannian VSI spaces

Abstract

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the ${\mathbf{S}}_i$- and $\mathbf{N}$-properties, and show that if the curvature tensors of the space possess the $\mathbf{N}$-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.

14 pages

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Cited by in corpus (8)

• Special Geometry and Space-time Signature
• Pseudo-Riemannian VSI spaces II
• 4D neutral signature VSI and CSI spaces
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Wick rotations and real GIT
• Quantum Klein Space and Superspace
• Mathematical Properties of a Class of Four-dimensional Neutral Signature Metrics
• Real GIT with applications to compatible representations and Wick-rotations