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Biharmonic submanifolds in spheres. (English) Zbl 1038.58011

Harmonic maps ϕ are critical points of the energy functional E(ϕ)=|dϕ| 2 , and ϕ is harmonic if and only if τ(ϕ)=0, where τ(ϕ) is the tension field of ϕ. Biharmonic maps are critical ones of the bienergy functional |τ(ϕ)| 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:
58E20Harmonic maps between infinite-dimensional spaces
53C43Differential geometric aspects of harmonic maps
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