On Ricci flat Supermanifolds

Details On Ricci flat Supermanifolds On Ricci flat Supermanifolds

2004-10-05

arxiv.org/abs/hep-th/0410047v2

JHEP0502:004,2005

Physics

High Energy Physics

High Energy Physics - Theory

9 pages; typos corrected

Scientific paper

10.1088/1126-6708/2005/02/004

We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci curvature implies the bosonic submanifold has vanishing scalar curvature. We prove that this phenomena is only restricted to fermionic complex dimension one. Further we conjecture that for complex fermionic dimension larger than one the Calabi-Yau theorem holds for supermanifolds.

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