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Let $(M,g)$ be a riemannian manifold and $\nabla^t$ connections parametrized by the real numbers. The connections have usual curvatures and Ricci curvatures $Ric(\nabla)$ and scalar curvature $r$. I define a Ricci flow of connections by:

$$\frac{\partial \nabla_X Y}{\partial t}= dr (X).Ric(\nabla) (Y)$$

Have we solutions of this flow for short time?

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