In complex manifold, one writes(adsbygoogle = window.adsbygoogle || []).push({});

$$ds^2=g_{ab}dz^adz^b\hspace{3cm}(1)$$

$$ds^2=2g_{\alpha\bar{\beta}}dz^{\alpha}d\bar{z}^{\bar{\beta}}+g_{\alpha\beta}dz^{\alpha\beta}dz^{\alpha}dz^{\beta}+g_{\bar{\alpha}\bar{\beta}}d\bar{z}^{\bar{\alpha}}d\bar{z}^{\bar{\beta}}\hspace{3cm}(2)$$

My question is why is there a "2" in the first term? Looks like two terms added up there but how come?

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# I Why do those two terms add here?

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