CMC proper-biharmonic surfaces of constant Gaussian curvature in spheres

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 $\sn^5$.

23 pages; some improvements, one section added

References in corpus (2)

• Biharmonic PNMC Submanifolds in Spheres
• Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries