# GR: FRW Metric relation between the scale factor & curvature

Mod note: OP warned about not using the homework template.
I have read that 'a(t) determines the value of the constant spatial curvature'..

Where a(t) is the scale factor, and we must have constant spatial curvature - this can be deduced from the isotropic at every point assumption.

I'm trying to see this from what I know, but I'm struggling...

Here's what I know:

The FRW metric takes the form:

## dt^{2}+a^{2}(t) ds^{2}, where ds^{2}=g_{ij}x^{i}x^{j}##, and ##g_{ij}## is the isotropic and homogenous spatial metric.

The Riemann tensor and metric are related via: