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The conformal invariant defined for compact Riemannian manifolds by Yamabe is generalized to pseudo-Riemannian manifolds and is shown to be nontrivial for Minkowski space. We also make some elementary remarks about generalizations of Yamabe’s equation to sections of vector bundles, as have been studied by physicists concerned with Goldstone bosons and the Higgs mechanism.

Conformal invariants of Minkowski space