关于具有平行平均曲率向量的子流形

On submanifolds with parallel mean curvature vector

通过对共形平坦空间中的Simons公式的代数估计,得到其中具有平行平均曲率向量的紧致子流形的一个拼挤性质.作为推论,讨论了单位球面中具有平行平均曲率向量的子流形的第二基本形式长度的拼挤问题,改进了已有的结论.

By the algebraic estimation to the Simons-Formula, a result of submanifolds with parallel mean curvature vector in a conformally flat Riemannian manifold is provided.As corollaries,some pinching problems on the submanifolds with parallel mean curvature vector in a unit sphere are discussed,which improves results obtained before.