Abstract
To comply with recent developments of path integrals in spaces with curvature and torsion, we find the correct variational principle for classical trajectories of spinless point-particles in such spaces. Although the action depends only on the length, the trajectories are autoparallels (straightest lines) rather than geodesics (shortest lines), due to the effects of a torsion force arising from a geometric peculiarity of the variational procedure.
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