2016 Volume 68 Issue 3 Pages 997-1024
Constant mean curvature (CMC) surfaces in spheres are investigated under the extra condition of biharmonicity. From the work of Miyata, especially in the flat case, we give a complete description of such immersions and show that for any h ∈ (0,1) there exist CMC proper-biharmonic planes and cylinders in $\mathbb S$5 with |H| = h, while a necessary and sufficient condition on h is found for the existence of CMC proper-biharmonic tori in $\mathbb S$5.
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