Biharmonic surfaces of constant mean curvature

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.

15 pages

References in corpus (1)

• Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries

Cited by in corpus (1)

• Biharmonic surfaces with parallel mean curvature in complex space forms