This is a follow up to a question about a four dimensional geometry that's suggested by data I've collected.
If I have a surface defined by:$$ds^2=-(\phi^2t^2)dt^2+dx^2+dy^2+dz^2$$where $\phi$ is a constant with units of $km$ $s^{-2}$, t is time ($s$), x, y and z are spatial coordiantes (in $km$), how would I calculate the curvature of the spatial surface?
Is the curvature zero (that is, does this metric describe perfectly flat space)?