For every Dubrovin-Novikov bracket of degree k, the k connections ∇[s] defined by the paper are flat.
Poisson cohomology o f scalar multidimensional Dubrovin–Novikov brackets
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On the structure of homogeneous local Poisson brackets
For every Dubrovin-Novikov bracket of degree k, the k connections ∇[s] defined by the paper are flat.