常曲率空间中的伪脐点子流形

Pseudo-umbilical Submanifolds in Spaces of Constant Curvature

本文研究常曲率Riemann流形中具有平行平均曲率的伪脐点子流形。得到了一个Simons型公式和一个相应的Pinching定理,并确定了球面中所有0≤S-nH^2≤n(H^2+C)/(2-1/P-1)的这类子流形或者是全脐点的,或者是Clifford环面,或者是Veroness曲面。

The pseudo-umbilical n-submanifolds with parallel mean ourvature in(n+p)-Riemannian manifold of constant curvature c are considered. A formula of Simons'type and therefore a Pinching theorem are obtained. It is proved that such submanifolds in a sphere with are totally umbilical submanifolds, Clifford minimal hypersurfaces in a hypersphere, or Veroness surfaces in 4-sphere.