局部对称共形平坦黎曼流形中紧致极小子流形的Ricci曲率

The Ricci Curvature of Compact Minimal Submanifolds in a Locally Symmetric Conformally Flat Riemannian Manifold

讨论了局部对称共形平坦黎曼流形中紧致极小子流形,得到了这类子流形第二基本形式模长平方关于外围空间Ricci曲率的Pinching定理,推广了相应的结果.

The compact minimal submanifold of a locally symmetric and comformally flat Riemannian manifold is investigated, and the Pinching theorems regarding the square of the length of the second fundamental form of the submanifolds and the outer space Ricci curvature are obtained,thus generalizing the corresponding results.