Biharmonic surfaces of constant mean curvature
Differential Geometry
2016-01-20 v1
Abstract
We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the Gaussian curvature on pseudo-umbilicity. Finally, the condition of biharmonicity is shown to enable an extension of the classical Hopf theorem to CMC surfaces in any ambient Riemannian manifold.
Keywords
Cite
@article{arxiv.1305.7020,
title = {Biharmonic surfaces of constant mean curvature},
author = {E. Loubeau and C. Oniciuc},
journal= {arXiv preprint arXiv:1305.7020},
year = {2016}
}
Comments
15 pages