Cartan's theory of geometric structure shows that torsionful connections compatible with a given metric are consistent alternatives, leaving affine structure underdetermined by the metric alone.
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Mathematical rules for comparing directions and measurements at different points in a curved space that include a property called 'torsion,' which describes a kind of twisting or spinning built into the space itself.
underdetermined(Used to contrast mathematical conjectures, whose correct answers are fixed by logical facts, with cases where no such determination exists.)
A decision or truth is underdetermined when logical facts alone do not fix a single correct answer.