# Vafa's semi-Ricci flat metric

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Cumrun Vafa and Greene-Shapere-Yau introduced semi-Ricci flat metric here:

B. Greene, A. Shapere, C. Vafa, and S.-T. Yau. Stringy cosmic strings and noncompact Calabi-Yau manifolds. Nuclear Physics B, 337(1):1–36, 1990

I know that such metrics are Kähler in fiber direction. Is there any counterexample to show that such metrics need not be not Kähler in horizontal direction?

This post imported from StackExchange MathOverflow at 2015-06-14 09:05 (UTC), posted by SE-user Hassan Jolany

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