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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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