LOCALLY SYMMETRICAL AND RIGID FACTORS FOR COMPLEX-MANIFOLDS VIA HARMONIC MAPS

We obtain a complete description of the Lie algebra of complete holomo rphic vector fields on the universal cover of a compact complex manifo ld with negative first Chern class. The main tools are an equivariance result we prove for harmonic maps and the rigidity theory for harmoni c maps from Kahler manifolds to locally symmetric spaces.