By using an inequality relation between a scalar curvature and the length of the second fundamental form, it is proved that sectional curvatures of a submanifold must be nonnegative (or positive).

利用数量曲率与第二基本形式长度之间的一个不等式关系，证明了其子流形的截面曲率一定非负(或者为正)，并将此应用到紧致子流形上，得到一些结果。

youdao

By using an inequality relation between a scalar curvature and the length of the second fundamental form, it is proved that sectional curvatures of a submanifold must be nonnegative (or positive).

利用数量曲率与第二基本形式长度之间的一个不等式关系，证明了其子流形的截面曲率一定非负(或者为正)，并将此应用到紧致子流形上，得到一些结果。

youdao