Graduate Ricci Form Notation: Need Help Understanding

[lichen1983312]

The material I am studying express the Ricci form as
$R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G$
where $G$ is the determinant of metric tensor, but I am not sure what does $\log G$ here, can anybody help?

 

[Ben Niehoff]

G is the determinant of the metric (the Riemannian metric, or the Hermitian metric? Pretty sure the latter, but it makes a difference). And log G is its logarithm. What part of it is confusing?

 

[lichen1983312]

Thanks for replying. Basically I was trying to ask the definition of logarithm of matrix when I was looking at the definition of Ricci form. The example I posted there is not a good one.

 

[Ben Niehoff]

But there is no logarithm of a matrix in the formula you posted. It's the logarithm of the determinant of a matrix.