Contact Calabi-Yau manifolds and Special Legendrian submanifolds
  We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional nilmanifolds. Finally we generalize to codimension $r$. 
Adriano Tomassini and Luigi Vezzoni