Let (M,g) be a riemannian manifold with Levi-Civita connection ∇LC acting on the tensor algebra. The codifferential on exterior forms is δ=⋆∘d∘⋆, with ⋆ the Hodge operator. Then, I define a flow on ω∈Λ2(TM):
∂ω∂t=∇LC(δω)∗ω
Can we find solutions of this flow for small times?