On the generalized Chen’s conjecture on biharmonic submanifolds. (English) Zbl 1268.58015
The generalized Chen’s conjecture on bi-harmonic submanifolds asserts that any bi-harmonic submanifold of a non-positively curved manifold is minimal. The authors show by an example that the conjecture is false. Examples of proper bi-harmonic submanifolds of non-positively curved spaces are given.
Reviewer: Aleksander Pankov (Baltimore)
MSC:
| 58E20 | Harmonic maps, etc. |
| 53C12 | Foliations (differential geometric aspects) |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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