  We explicitly construct noncommutative * products on circularly symmetric two
dimensional space by using the technique of Fedosov's deformation quantization.
Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) and
su(1,1) algebra respectively. These are candidates of * products applicable to
noncommutative field theories or noncommutative gauge theories on spaces with
nontrivial symplectic structure.
