String theory, Calabi–Yau manifolds, complex dimensions

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Spinnor
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I am not sure what you are searching for
With your help, to understand more!

An even dimensional real manifold does not necessarily translates to Half the real dimension Complex manifold, in fact there would be a proper subset of Real manifolds which will translate to Complex Manifolds.
So can I say that complex manifolds are a more diverse and rich group of manifolds then real manifolds?

Thanks!
 

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