D-Branes in Curved Space

We obtain actions for N D-branes occupying points in a manifold with arbitrary Kahler metric. In one complex dimension, the action is uniquely determined (up to second order in commutators) by the requirement that it reproduce the masses of stretched strings and by imposing supersymmetry. These conditions are very restrictive in higher dimensions as well. The results provide a noncommutative extension of Kahler geometry.