关于球面的紧子流形

On Compact Submanifolcls in a Sphere

中文摘要:

      本文讨论单位球面的紧致子流形的Pinching问题.改进了S.T.Yan与莫小欢有关球面中具有平行平均曲率的紧致子流形的Pinching常数及S.S.Chern等与沈一兵有关紧致极小子流形的Pinching常数.对截曲率的情形,本文还改进了沈一兵有关截曲率的Pinching常数.

英文摘要:

      In this paper the Pinching theory for compact submanifolds in a unit sphere is considered. We improve the Pinching constants of S.T. Yau and X.H. Mo for compact submanifolds with parallel mean curvature in sphere and those of S.S. Chern and Y.B. Shen for compact minimal submanifolds. For sectional curvature, we improve the Pinching constant of Y.B. Shen.