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May 28, 2018 at 12:33 comment added user74900 John, kind of late, but it appears that the variation equation you've written does not quite hold for non-CY manifolds. Proposition 1.6.1 in Smoczyk's Habilitation thesis gives formula with a term proportional to Ricci curvature of the ambient manifold. This final conclusion is still correct though
Aug 11, 2017 at 13:08 history answered Arctic Char CC BY-SA 3.0