Noncommutative Particles in Curved Spaces

We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity ${\theta }^{\mu \nu }$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a noncommutative first-order action in D=10 curved spacetime and the covariant equations of motions were computed. This model, invariant under diffeomorphism, generalizes recent relativistic results.