The length of harmonic forms on a compact Riemannian manifold
The length of harmonic forms on a compact Riemannian manifold
We study $(n+1)$-dimensional Riemannian manifolds with harmonic forms of constant length and first Betti number equal to $n$ showing that they are $2$-step nilmanifolds with some special metrics. We also characterize, in terms of properties on the product of harmonic forms, the left-invariant metrics among them. This allows us to …