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Hypersurfaces in $$E^ 4$$ with harmonic mean curvature vector field. (English) Zbl 0839.53007
Given an immersion in the Euclidean space $$x:M \to \mathbb{R}^m$$, it is well known that the immersion is harmonic, i.e. $$\Delta x=0$$, if and only if $$M$$ is minimal. In this paper the author studies biharmonic immersions, i.e. such that $$\Delta^2 x=0$$. He proves that $$M$$ is a biharmonic hypersurface in $$\mathbb{R}^4$$ if and only if $$M$$ is a minimal hypersurface.

##### MSC:
 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
##### Keywords:
biharmonic immersions; minimal hypersurface
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##### References:
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