• Curvature operators and scalar curvature invariants 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2010)
      We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant deriva- tives). ...
    • Discriminating the Weyl type in higher dimensions using scalar curvature invariants 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011)
      We consider higher dimensional Lorentzian spacetimes which are currently of interest in theoretical physics. It is possible to algebraically classify any tensor in a Lorentzian spacetime of arbitrary dimensions using ...
    • Higher dimensional bivectors and classification of the Weyl operator 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2010)
      We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consis- tent with its boost-weight decomposition. We then algebraically classify the Weyl ...
    • Note on the invariant classification of vacuum type D spacetimes 

      Coley, Alan; Hervik, Sigbjørn (Journal article; Peer reviewed, 2009-12)
      We illustrate the fact that the class of vacuum type D spacetimes which are I-non-degenerate are invariantly classified by their scalar polynomial curvature invariants.
    • On the algebraic classification of pseudo-Riemannian spaces 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011-12)
      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 Si- and N-properties) and present a ...
    • Pseudo-Riemannian VSI spaces 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011)
      In this paper we consider pseudo-Riemannian spaces of arbitrary sig- nature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces ...