On the algebraic classification of pseudo-Riemannian spaces

Abstract

We consider arbitrary-dimensional pseudo-Riemannian spaces of signature $(k,k+m)$. We introduce a boost-weight decomposition and define a number of algebraic properties (e.g., the ${\mathbf{S}}_i$- and $\mathbf{N}$-properties) and present a boost-weight decomposition to classify the Weyl tensors of arbitrary signature and discuss degenerate algebraic types (e.g., VSI spaces). We consider the four dimensional neutral signature space as an illustration.

7 pages

References in corpus (6)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Spacetimes characterized by their scalar curvature invariants
• Kundt Spacetimes
• Higher dimensional VSI spacetimes
• Higher dimensional bivectors and classification of the Weyl operator
• Curvature operators and scalar curvature invariants

Cited by in corpus (5)

• Pseudo-Riemannian VSI spaces II
• $\mathcal{I}$-degenerate pseudo-Riemannian metrics
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Wick rotations and real GIT
• Real GIT with applications to compatible representations and Wick-rotations