CMC proper-biharmonic surfaces of constant Gaussian curvature in spheres

E. Loubeau; C. Oniciuc

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arXiv · 1403.1703

CMC proper-biharmonic surfaces of constant Gaussian curvature in spheres

E. Loubeau·C. Oniciuc

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Abstract

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 $\sn^5$ with $|H|=h$, while a necessary and sufficient condition on $h$ is found for the existence of CMC proper-biharmonic tori in $\sn^5$.

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BibTeX RIS

E. Loubeau, C. Oniciuc. 2014-03-07. CMC proper-biharmonic surfaces of constant Gaussian curvature in spheres. https://arxiv.org/abs/1403.1703

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