Abstract
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.
Citation
Martin Roček. Neal Wadhwa. "On Calabi-Yau supermanifolds." Adv. Theor. Math. Phys. 9 (2) 315 - 320, April 2005.
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