# A Notation in Ricci form

Tags:
1. Oct 17, 2016

### 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?

2. Oct 17, 2016

### 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?

3. Oct 18, 2016

### lichen1983312

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

4. Oct 19, 2016

### 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.