Advances in Theoretical and Mathematical Physics
Volume 9 (2005)
On Calabi-Yau supermanifolds
Pages: 315 – 320
We prove that a Kähler 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.
2010 Mathematics Subject Classification
Primary 32Q25. Secondary 32C11.
Published 1 January 2005