While Minkowski space and Euclidean space both have identically zero curvature tensors it seems that a flat Lorentz manifold in general, may not admit a flat Riemannian metric. Such a manifold is the quotient of Minkowski space by the action of a properly discontinuous group of Lorentz isometries. This group in general is not a subgroup of the group of rigid motions of Euclidean space and so can not have a flat Riemannian metric.(adsbygoogle = window.adsbygoogle || []).push({});

What can one say about the curvature of Riemannian metrics on flat Lorentz manifolds?

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# A Curvature of Flat Lorentz manifolds

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