Let (M,g) be a riemannian manifold and ∇t connections parametrized by the real numbers. The connections have usual curvatures and Ricci curvatures Ric(∇) and scalar curvature r. I define a Ricci flow of connections by:
∂∇XY∂t=dr(X).Ric(∇)(Y)
Have we solutions of this flow for short time?