A theory that allows for the break of the Lorentz symmetry in the tangent space-time within a Riemannian geometric framework was studied.The conclusion is that the Riemannian geometry is not compatible with the absence of an exact Lorentz symmetry in the tangent space-time.If one wants to explore the consequences of Lorentz symmetry breaking in four dimensions other ways must be tried and/or a higher number of dimensions must be considered.
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