摘要
推广了Lawson和Simons关于标准球面上不存在稳定流的著名结论,证明了如下结果:设M是欧氏空间的n(≥3)维紧致子流形,R和S分别为M的数量曲率和第二基本形式长度平方,如果R>(n—2)S,则M上不存在任何稳定流,从而一些同调群和同伦群消失,同时还给出了Lawson-Simons猜想的部分肯定回答。
We prove that there do not exist any stable integral currents in some kinds of submanifolds in the Euclidean space and generalize the result due to Lawson and Simons We also derive the topological character of these submanifolds.
关键词
数量曲率
同调群
稳定流
子流形
Scalar curvature, Homology group, Stable integral current
