On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds
  Let X be a Calabi-Yau threefold. We show that if there exists on X a non-zero nef non-ample divisor then X contains a rational curve, provided its second Betti number is greater than 4. 
Simone Diverio and Andrea Ferretti
math.AG math.CV