Flat deformation theorem and symmetries in spacetime

Mathematics

Scientific paper

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Numerical Approximation And Analysis, Approximation Methods, Equations Of Motion, Riemannian Geometries

Scientific paper

The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally it can always be written in terms of a semi-Riemannian flat metric ɛ, a two-form F and a scalar function c fulfilling a prescribed scalar constraint, say Ψ(c,F,x) = 0. Here we show that if the original metric g admits a Killing vector, then the deformation may be carried out in a way such that the flat deformed metric `inherits' that symmetry.

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