Isospectral hypersurfaces in Euclidean spheres

Abstract

The aim of this work is to present a classification of some compact hypersurfaces $M^{n}$ of a unit sphere $S^{n+1}$ provided the spectra of the Laplacian of $p$-forms of $M^{n}$, which we denote by $\mathrm{Spec}^p(M)$, is equal to the spectra $\mathrm{Spec}^p(M_0)$, of a given hypersurface $M_{0}^{n}$.