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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
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