  Let X be a smooth cubic threefold. We can associate two objects to X: the
intermediate Jacobian J and the Fano surface F parametrising lines on X. By a
theorem of Clemens and Griffiths, the Fano surface can be embedded in the
intermediate Jacobian and the cohomology class of its image is minimal. In this
paper we show that if X is generic, the Fano surface is the only surface of
minimal class in J.
