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Biharmonic submanifolds in spheres. (English) Zbl 1038.58011

Harmonic maps $\phi$ are critical points of the energy functional $E\left(\phi \right)={\int |d\phi |}^{2}$, and $\phi$ is harmonic if and only if $\tau \left(\phi \right)=0$, where $\tau \left(\phi \right)$ is the tension field of $\phi$. Biharmonic maps are critical ones of the bienergy functional ${\int |\tau \left(\phi \right)|}^{2}$.

The authors study biharmonic maps into a manifold $N$ of constant curvature, in particular an $n$-dimensional standard sphere. This paper consists of two parts: (1) non-existence results of non-harmonic biharmonic maps. (2) examples of non-harmonic biharmonic maps.

##### MSC:
 58E20 Harmonic maps between infinite-dimensional spaces 53C43 Differential geometric aspects of harmonic maps
##### Keywords:
biharmonic map; sphere
##### References:
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