Moving from a theory that allows for the break of the Lorentz symmetry in the tangent space-time within a Riemannian geometric framework, this paper looks for the admissible values of the parameters that measure the break. These values are explicitly worked out in some special cases and it is shown that all of them must be zero. 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.