  Starting with the first-order singular Lagrangian, the canonical structures
of the noncommutative quantum system on a submanifold embedded in the
higher-dimensional Euclidean space are investigated with the projection
operator method (POM) and the Dirac-bracket formulation in the case of the
derivative-type constraint. Using the successive projection procedure and the
iterativity of the Dirac bracket, the noncommutative quantum system is
constructed in the form including all orders of the
noncommutativity-parameters. When the noncommutative quantum system is
constrained to a curved space, the commutator algebra of the system is
presented within the 1st-order approximation with respect to Dirac-const. and
the noncommutativity-parameters.
