Isospectral hypersurfaces in Euclidean spheres

Abstract

The aim of this work is to present a classification of some compact hypersurfaces Mⁿ of a unit sphere Sⁿ⁺¹ provided the spectra of the Laplacian of p-forms of Mⁿ, which we denote by Spec^p(M), is equal to the spectra Spec^p(M₀), of a given hypersurface M₀ⁿ.