Can anyone help me and prove that in the case of the Ricci flow, the symmetries of the flow are scalings and diffeomorphisms?
Thanks for your time.
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I apologise first for submitting this comment as an answer (not enough MO-cred to comment) and second for submitting a question rather than a comment:
What I can gather from the comments above is that the symmetries of the Ricci flow are completely understood: Every `symmetry' of the Ricci flow is a spatial diffeomorphism combined with scaling (and every such combination is a symmetry). My question is whether the problem is also solved for the mean curvature flow (of, say, hypersurfaces of Euclidean space)?