  A form of the constraints, specifying a $D$-dimensional manifold embedded in
$D+1$ dimensional Euclidean space, is discussed in the path integral formula
given by a time discretization. Although the mid-point prescription is
privileged in the sphere $S^D$ case, it is more involved in generic cases. An
interpretation on the validity of the formula is put in terms of the operator
formalism. Operators from this path integral formula are also discussed.
