Abstract.
Let H, K and R be, respectively, the mean curvature, the Gauss–Kronecker curvature and the scalar curvature of a closed hypersurface immersed in the unit sphere \(\mathbb{S}^4\). In this paper we completely classify the closed hypersurfaces of \(\mathbb{S}^4\) where any two of H, K and R are constant.
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Editorial Note: F. G. B. Brito was invited to deliver a principal adress on the topic of this paper at the Conference Differential Geometry at the Banach center, Poland, September 2005.
Submitted: September 30, 2005. Revised: November 25, 2005.
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de Almeida, S.C., Brito, F.G.B. & de Sousa, L.A.M. Closed Hypersurfaces of \(\mathbb{S}^4\) with Two Constant Curvature Functions. Result. Math. 50, 17–26 (2007). https://doi.org/10.1007/s00025-006-0232-2
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DOI: https://doi.org/10.1007/s00025-006-0232-2