Rigidity theorem for hypersurfaces in a unit sphere
By investigating hypersurfaces \(M^n\) in the unit sphere \(S^{n+1} (1)\) with \(H_k=0\) and with two distinct principal curvatures, the authors provide a characterization of the torus \(S^1(\sqrt{k/n})\times S^{n-1} (\sqrt{(n-k)/n})\). They extend recent results of \textit{O. Perdomo} [Arch. Math. 82, 180--184 (2004; Zbl 1062.53055), \textit{Q. Wang}, Monatsh. Math. 140, No. 2, 163--167 (2003; Zbl 1066.53112), and \textit{T. Otsuki}, Am. J. Math. 92, 145--173 (1970; Zbl 0196.25102)].
scientific article; zbMATH DE number 5118925