Kaehler manifolds with numerically effective Ricci class and maximal   first Betti number are tori
  Let M be an n-dimensional K\"ahler manifold with numerically effective Ricci class. In this note we prove that, if the first Betti number b_1(M)=2n, then M is biholomorphic to the complex torus T^n_C. 
Fuquan Fang