Abstract
We have shown previously that an invariance principle is defined in curved space by invariance under the Brandt groupoid consisting of elements given by parallel displacements along all possible curves in space-time. It is argued here that the Brandt groupoid might contain the Poincare group as a local group in each tangent space but then space-time must have non-vanishing torsion. Such a conclusion might also be implied by recent measurements ofSadeh et al. For an Einstein manifold, on the other hand, the Brandt groupoid contains only the homogeneous Lorentz group.
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