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Mar 10, 2012 at 17:04 comment added BS. And I realize that even dimension 3 isn't in the OP (nor completeness of the CY, by the way).
Mar 10, 2012 at 16:59 history edited BS. CC BY-SA 3.0
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Mar 10, 2012 at 16:19 comment added BS. I agree this is the real question, but since the OP didn't mention compactness I assumed he didn't know R. Bryant's result.
Mar 10, 2012 at 12:00 comment added Ben McKay Only if you consider noncompact Calabi-Yau manifolds; see page 3. The real question is about compact Calabi-Yau manifolds.
Mar 10, 2012 at 11:09 history answered BS. CC BY-SA 3.0