Let (M,gt) be a riemannian manifold with riemannian curvature R(g) and scalar curvature r(g), I define:
Xg=dr(g)∗
then I can define a flow over metrics:
∂g∂t(X,Y)=R(g)(X,Xg,Y,Xg)
It is symmetric in X,Y.
Is this flow well defined? Have we singularities for the flow?