Abstract
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 $h \in (0,1)$ 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 ${\mathbb S}^5$.
Citation
Eric LOUBEAU. Cezar ONICIUC. "Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres." J. Math. Soc. Japan 68 (3) 997 - 1024, July, 2016. https://doi.org/10.2969/jmsj/06830997
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