论文标题
在单位球体中具有恒定标态曲率$ n（n-1）$的完整超曲面上
On complete hypersurfaces with constant scalar curvature $n(n-1)$ in the unit sphere
论文作者
论文摘要
令$ m^n $为$ n $ dimensional完整且本地平面的hypersurface在单位球体中$ \ mathbb {s}^{n+1} $，具有常数标量曲率$ n（n-1）$。我们表明，如果总曲率$ \ left（\ int _ {m} | h | ^ {n} d v \ right） ^ {\ frac {\ frac {1} {n}} $ of $ m $很小，那么$ m ^ n $是完全geodesic的。
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.
