  Let $M^n$ be an $n$-dimensional complete and locally conformally flat
hypersurface in the unit sphere $\mathbb{S}^{n+1}$ with constant scalar
curvature $n(n-1)$. We show that if the total curvature $\left( \int _ { M } |
H | ^ { n } d v \right) ^ { \frac { 1 } { n } }$ of $M$ is sufficiently small,
then $M^n$ is totally geodesic.
