数量曲率、截面曲率及其应用(英文)

Scalar Curvature,Sectional Curvature and Its Application

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.

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). Some results can be obtained with its application to compact submanifolds.