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全拟脐子流形中的稳定积分流
引用本文:张学山. 全拟脐子流形中的稳定积分流[J]. 数学进展, 2001, 30(5): 435-442
作者姓名:张学山
作者单位:上海工程技术大学数学教研室,
摘    要: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。

关 键 词:稳定积分流 全拟脐子流形 超曲面 形算子 同调群 黎曼流形 Lawson-Simons猜想
修稿时间:1999-04-02

On Stable Integral Currents in Totally Quasi-umbilical Submanifolds
Zhang Xueshan. On Stable Integral Currents in Totally Quasi-umbilical Submanifolds[J]. Advances in Mathematics(China), 2001, 30(5): 435-442
Authors:Zhang Xueshan
Abstract: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.
Keywords:stable integral current  totally quasi-umbilical submanifold  hypersurface  shape operator  homology group
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