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Biharmonic submanifolds in spheres. (English) Zbl 1038.58011
Harmonic maps $$\phi$$ are critical points of the energy functional $$E(\phi ) = \int | d\phi | ^2$$, and $$\phi$$ is harmonic if and only if $$\tau ( \phi) = 0$$, where $$\tau (\phi )$$ is the tension field of $$\phi$$. Biharmonic maps are critical ones of the bienergy functional $$\int | \tau( \phi )| ^2$$.
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, etc. 53C43 Differential geometric aspects of harmonic maps
##### Keywords:
biharmonic map; sphere
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##### References:
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