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Biharmonic submanifolds in spheres. (English) Zbl 1038.58011
Harmonic maps $\phi$ are critical points of the energy functional $E(\phi ) = \int \vert d\phi \vert ^2$, 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 $\int \vert \tau( \phi )\vert ^2$. 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.

58E20Harmonic maps between infinite-dimensional spaces
53C43Differential geometric aspects of harmonic maps
Full Text: DOI
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