Rigidity theorems of Clifford torus
Let \(M\) be a closed minimal hypersurface of constant scalar curvature or of constant Gauss-Kronecker curvature in \(S^{n+1}\). The author proves that if \((n-1)\) principal curvatures have the same sign, then \(M\) is congruent to a Clifford torus \(S^1\left(\sqrt{\frac{1}{n}}\right)\times S^{n-1}\left(\sqrt{\frac{n-1}{n}}\right)\).
scientific article; zbMATH DE number 1672704