On Calabi-Yau supermanifolds
arXiv:hep-th/0408188
Abstract
We prove that a Kahler supermetric on a supermanifold with one complex fermionic dimension admits a super Ricci-flat supermetric if and only if the bosonic metric has vanishing scalar curvature. As a corollary, it follows that Yau's theorem does not hold for supermanifolds.
4 pages