401 citations · 2.9k across the 98 of their papers we have counts for
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Real GIT with applications to compatible representations and Wick-rotations
Christer Helleland, Sigbjorn Hervik
Motivated by Wick-rotations of pseudo-Riemannian manifolds, we study real geometric invariant theory (GIT) and compatible representations. We extend some of the results from earlie…
On a new class of infinitesimal group actions on pseudo-Riemannian manifolds
Sigbjørn Hervik
Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a gro…
Pseudo-Riemannian VSI spaces II
Sigbjorn Hervik
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). Using an algebraic classificatio…
A Wick-rotatable metric is purely electric
Christer Helleland, Sigbjorn Hervik
We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tenso…
-degenerate pseudo-Riemannian metrics
Sigbjorn Hervik, Anders Haarr, Kei Yamamoto
In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invaria…
4D neutral signature VSI and CSI spaces
A. Alcolado, A. MacDougall, A. Coley +1
In this paper we present a number of four-dimensional neutral signature exact solutions for which all of the polynomial scalar curvature invariants vanish (VSI spaces) or are all c…