A new characterization for Clifford hypersurfaces (Q6635279)

The authors classify Clifford hypersurfaces by the invariant \( \sigma_k=\frac{\int_M (|A|^2)^k}{|M|} \), which is defined for a closed minimal immersed hypersurface \( M \) in \( S^{n+1} \) with second fundamental form \( A \). Using this invariant, they are able to distinguish non-totally geodesic 2-dimensional surfaces \( M \). They also obtain conditions on \(\sigma_k\) for hypersurfaces \(M\) with two distinct principal curvatures when \( n \geq 3 \).