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.


58E20 Harmonic maps, etc.
53C43 Differential geometric aspects of harmonic maps
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