## The spectrum of the Laplacian for 5-forms.(English)Zbl 0553.58035

Let (M,g) and (M’,g’) be compact orientable Riemannian manifolds with the same spectrum of the Laplacian for 5-forms. We prove that, for dim M$$=7$$ and dim M$$=14,15,...,432$$, (M,g) is of constant curvature if and only if (M’,g’) is so.

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 53C20 Global Riemannian geometry, including pinching