On Calabi-Yau supermanifolds
classification
✦ hep-th
math.DG
keywords
supermanifoldssupermetricadmitsbosoniccalabi-yaucomplexcorollarycurvature
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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.
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