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

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

2009-02-27

arxiv.org/abs/0902.4849v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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 $\mathbb{S}^3(\frac{1}{\sqrt{2}})$.

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