Real GIT with applications to compatible representations and Wick-rotations

Abstract

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 earlier works \cite{W2,W1}, in particular, we give some sufficient as well as necessary conditions for when pseudo-Riemannian manifolds are Wick-rotatable to other signatures. For arbitrary signatures, we consider a Wick-rotatable pseudo-Riemannian manifold with closed $O(p,q)$-orbits, and thus generalise the existence condition found in \cite{W1}. Using these existence conditions we also derive an invariance theorem for Wick-rotations of arbitrary signatures.

30 pages, to appear in J. Geom. Phys

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• Metrics With Vanishing Quantum Corrections
• Higher dimensional VSI spacetimes
• Type II universal spacetimes
• Pseudo-Riemannian VSI spaces II
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• Pseudo-Riemannian VSI spaces
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Cited by in corpus (1)

• Wick-rotations of pseudo-Riemannian Lie groups