Resumen de Isometries of the Teichmüller metric
We study the curvature properties of the Kobayashi-Teichriiuller metric showing in particular that the holomorphic curvature is constant -4. Carrying a program due to Royden, we describe the consequences on complex geodesics. The results are applied to characterize biholomorphic maps into Teichmfller spaces in finite and infinite dimension.
