# A compute of Ricci Flow

Let $g(0)=g_0$ and $Ric(g_0)=\lambda g_0,\lambda\in\mathbb{R}$, the $Ric(g)$ is the Ricci curvature,$g$ is Riemannian metric. How to show that :

The $g(t)=(1-2\lambda t)g_0$ is a solution of $$\frac{\partial g}{\partial t}=-2Ric(g)$$

Thanks for any detail answer or hint.