Scalar curvature of hypersurfaces with constant mean curvature in spheres

LetM be a closed hypersurface with constantmean curvature H in a unit sphere space S
ⁿ⁺¹
, n ≤ 5, and S the square of the length of the second fundamental form of M. If | H | < ∈ (n), then there exists δ(n, H) > 0 such that if
$n+(n^{3})/(n-1)H^{2}+(n(n-2))/(2(n-1))\sqrt{n^{2}H^{4}+4(n-1)H^{2}}\leq S \leq n + (n^{3})/(2(n-1))H^{2}+(n(n-2))/(2(n-1))\times \sqrt{n^{2}H^{4}+4(n-1)H^{2}}+\delta (n, H)$
, then
$S\equiv n+ (n^{3})/(2(n-1))H^{2}+(n(n-2))/(2(n-1))\sqrt{n^{2}H^{4}+(n-1)H^{2}}$
and these hypersurfaces are determined, where ∈ (n) is a constant depending only on n. In the case H ≡ 0, Peng-Terng ts result is recovered.