We consider a generalization of Calabi-Yau structures in the context of 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 $r$.
"Contact Calabi-Yau manifolds and special Legendrian submanifolds." Osaka J. Math. 45 (1) 127 - 147, March 2008.