Biharmonic surfaces of ${\mathbb{S}}^4$

Abstract

In this note we prove that a constant mean curvature surface is proper-biharmonic in the unit Euclidean sphere ${\mathbb{S}}^4$ if and only if it is minimal in a hypersphere ${\mathbb{S}}^3(\frac{1}{\sqrt{2}})$.

6 pages

References in corpus (1)

• A short survey on biharmonic maps between Riemannian manifolds

Cited by in corpus (1)

• Biharmonic PNMC Submanifolds in Spheres