Biharmonic conjectures on hypersurfaces in a space form. (English) Zbl 07772564
Summary: We apply the Murnaghan-Nakayama rule in the representation theory of symmetric groups to develop new techniques for studying biharmonic hypersurfaces in a space form. As applications of the new techniques, we settle the well-known Chen’s conjecture on biharmonic hypersurfaces in \(\mathbb{R}^6\) and BMO conjecture on biharmonic hypersurfaces in \(\mathbb{S}^6\).
MSC:
| 53C40 | Global submanifolds |
| 58E20 | Harmonic maps, etc. |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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