The gap of the eigenvalues for p-forms and harmonic p-forms of constant length

We study the k th positive eigenvalue λk(p)(M,g) of the Laplacian on p-forms for a connected oriented closed Riemannian manifold (M,g). If all non-trivial harmonic p-forms on (M,g) have constant length, then it follows that λk(p)(M,g)≤λk(0)(M,g) for all k≥1.