  The geometrical representation of the Jacobian in the path integral reduction
problem which describes a motion of the scalar particle on a smooth compact
Riemannian manifold with the given free isometric action of the compact
semisimple Lie group is obtained. By using the formula for the scalar curvature
of the manifold with the Kaluza--Klein metric, we present the Jacobian as
difference of the scalar curvature of the total space of the principal fibre
bundle and the terms that are the scalar curvature of the orbit space, the
scalar curvature of the orbit, the second fundamental form of the orbit and the
square of the principle fibre bundle curvature.
