Advances in Theoretical and Mathematical Physics

Volume 9 (2005)

Number 2

On Calabi-Yau supermanifolds

Pages: 315 – 320



Martin Roček

Neal Wadhwa


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