Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal en- tropy is absolutely continuous with respect to Lebesgue measure. RESUME. Nous classons les surfaces complexes projectives munies d'un automorphisme dont l'unique mesure d'entropie maximale est absolument continue par rapport a la mesure de Lebesgue.