Isospectral hypersurfaces in Euclidean spheres
Let \(M\) be a compact Riemannian manifold without boundary of dimension \(n\) and \(\text{Spec}^{p}(M):=\{0\leq \lambda_{0}^{p}\leq \lambda_{1}^{p},\dots\uparrow +\infty\}\), \(p=0,1,\dots,n,\) be the spectrum of the Laplacian p-forms in \(M\). If \(\text{Spec}^{p}(M)=\text{Spec}^{p}(M_{0})\) for a given hypersurface \(M_{0}\) then classification results for \(M\) are given. Denote by \(H, H_{0}\) the mean curvature of \(M\), \(M_{0}\) respectively. The case \(H=H_{0}=0,\) is studied and he showed that the assumption \(H=H_{0}\) in [\textit{J. Wang}, J. Math. Res. Expo. 17, No. 4, 496--500 (1997; Zbl 0915.53027)] is not necessary,
scientific article; zbMATH DE number 2157856