全拟脐子流形中的稳定积分流

1973年，H.B.Lawson和J.Simons猜想，在任何紧致，单连通，1／4－pinched黎曼流形中，不存在稳定积分流，本文研究全拟脐子流形中稳定积分流的不存在性，证明了在一定几何条件下，这类流形中不存在稳定积分流，由此得到几个同调群的消设定理，所得结果表明，Lawson-Simons猜想对于拟脐超曲面和某些全拟脐子流形是对的。

On Stable Integral Currents in Totally Quasi-umbilical Submanifolds

In 1973, H. B. Lawson and 3. Simons conjectured that there are no stable integral currents in any compact, simply connected Riemannian manifold which is 1/4-pinched. Let M be a totally quasi-umbilical submanifold immersed in a space form. In this paper, we study nonexistence of stable integral currents in M and prove that under some geometric conditions there is no stable integral p-current in M and the homology group Hp(M, Z) =0. The obtained results show that the Lawson-Simons conjecture is right for quasi-umbilical hypersurfaces and for some totally quasiumbilical submanifolds.