| 球面中不稳定的高阶极小Clifford超曲面低指标的刻画 |
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| 引用本文： | 曹林芬,戴朝晖.球面中不稳定的高阶极小Clifford超曲面低指标的刻画[J].河南师范大学学报(自然科学版),2014(4):13-17. |
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| 作者姓名： | 曹林芬 戴朝晖 |
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| 作者单位： | 河南师范大学数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金(U1304101;11171091);河南省科技厅基础与前沿项目(132300410141) |
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| 摘 要： | 根据单位球面中不稳定的高阶极小子流形的一个充分条件,构造了球面中一类不稳定的r-极小超曲面,即所谓的n维r-极小Clifford超曲面C1,n-1(r)=S1(r+1/n)(1/2)×Sn-1(n-r-1/n)(1/2),这里r是偶数,且r∈{0,1,…,n-1}.特别地,通过计算2-极小Clifford超曲面C1,n-1(2)的Jacobi算子的第二特征值,得到当n4时,其稳定性指标Ind2(C1,n-1(2))≥3n+3.
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| 关 键 词： | r-极小子流形 Lr算子 稳定性指标 Clifford超曲面 |
A Characterization of Low Index of Unstable r-minimal Clifford Hypersurfaces in Spheres |
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| CAO Linfen;DAI Zhaohui.A Characterization of Low Index of Unstable r-minimal Clifford Hypersurfaces in Spheres[J].Journal of Henan Normal University(Natural Science),2014(4):13-17. |
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| Authors: | CAO Linfen;DAI Zhaohui |
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| Institution: | CAO Linfen;DAI Zhaohui;College of Mathematics and Information Science,Henan Normal University; |
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| Abstract: | According to a sufficient condition of unstable higher-order minimal submanifolds in spheres,the authors construct a family of unstable r-minimal submanifolds,that is so-called r-minimal Clifford hypersurfaces C1,n-1(r)=S1(r+1/n)(1/2)×Sn-1(n-r-1/n)(1/2),here r is evenand r∈ {0,1,…,n-1}.In particular,by computing the second eigenvalue ofJacobi operator of 2-minimal Clifford hypersurfaces C1,n-1(2),the authors obtain that when n4,the stability index Ind2(C1,n-1(2))≥3n+3. |
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| Keywords: | r-minimal submanifolds Lroperator stability index Clifford hypersurfaces |
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