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The geometrical representation of the path integral reduction Jacobianobtained in the problem of the path integral quantization of a scalar particlemotion on a smooth compact Riemannian manifold with the given free isometricaction of the compact semisimple Lie group has been found for the case when thelocal reduced motion is described by means of dependent coordinates. The resultis based on the scalar curvature formula for the original manifold which isviewed as a total space of the principal fibre bundle.

journal of geometry and physics

On the geometrical representation of the path integral reduction  Jacobian: The case of dependent coordinates in the description of the reduced  motion