Abstract.
By investigating hypersurfaces M n in the unit sphere S n+1(1) with H k = 0 and with two distinct principal curvatures, we give a characterization of torus the \(S^1(\sqrt{k/n})\times S^{n-1}(\sqrt{(n-k)/n})\). We extend recent results of Perdomo [9], Wang [10] and Otsuki [8].
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Wei, G. Rigidity Theorem for Hypersurfaces in a Unit Sphere. Mh Math 149, 343–350 (2006). https://doi.org/10.1007/s00605-005-0378-0
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DOI: https://doi.org/10.1007/s00605-005-0378-0