## Quadric representation and Clifford minimal hypersurfaces.(English)Zbl 0818.53076

It is proved that the Clifford minimal hypersurfaces in the $$(n+1)$$- dimensional unit hypersphere are the only compact, minimal and non- totally geodesic spherical hypersurfaces possessing the following property: Its quadric representation is mass-symmetric in some hypersphere and minimal in some concentric hyperquadric.

### MSC:

 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C40 Global submanifolds
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