A hermitian metric satisfies tex2html_wrap80 for tex2html_wrap81 the almost complex structure. This means tex2html_wrap82 with the other components of the complex metric unrestricted.

If M is a complex manifold with Riemmannian metric g, you can make a hermitian metric by tex2html_wrap83

if tex2html_wrap84 the tex2html_wrap85 is a 2-form called the kahler form

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