Let $g=\text d t^2+ \gamma_t$ be the metric of a Riemann manifold $M$ of dimension 3 , where $\gamma_t$ is the metric on the surface $\Sigma_t=\partial M$.
If $\hat{g}=\rho^2(t)\text dt^2+\gamma_t$
then the scalar curvature $\hat{R}$ of $\hat{g}$ is
$\hat{R}(t,x)=\frac{1}{\rho^2(t)}(R(t,x)+2K(t,x)(\rho^2(t)-1)+\frac{2\rho'(t)}{\rho(t)}H(t,x))$
where $K(t,x)$ and $H(t,x)$ are the Gauss and mean curvature of $\Sigma_t$ with respect to $g$ respectively.
Here I don't know how to calculate $\hat{R}$ ,I need someone to help me .