欧氏空间和球面子流形中Yang-Mills场的一类不稳定性结果
被引量:1
Some Results on Instability of Yang-Mills Field of Submanifolds in Euclidean Space and Standard Sphere
摘要
本文就欧氏空间和球面中紧致子流形的Yang-Mills场进行了讨论.得到了一类不稳定性结果.
The authors discuss the stability of Yang-Mills field of compact submanifolds in Euclidean space Rn+pand sphere Sn+prespectively, and present some results on its instability.
基金
国家自然科学基金部分资助项目(19971060)
河南省自然科学基金(004051900)
河南省教委资助项目(9711006)
参考文献16
-
1BOURGUIGNON J P, LAWSON H B Jr. Stability and isolation phenomenon for Yang-Mills fields [J]. Comm. Math. Phys. , 1981, 79: 189-230.
-
2BOURGUIGNON J P, LAWSON H B Jr, SIMONS J. Stability and gap phenomenon of Yang-Mills field [J]. Proc. Natl. Acad. Sci. USA. , 1979, 76: 1550-1553.
-
3LAQUER H T. Stability properties of the Yang-Mills functional near the canonical connection [J].Michigan Math. J. , 1984, 31: 139-159.
-
4KOBAYASHI S, OHNITA Y S, TAKEUCHI M. On instability of Yang-Mills Connections [J]. Math.Z., 1986, 193: 165-189.
-
5KOBAYASHI S, NOMIZU K. Foundations of Differential Geometry [M], Vol. I, Interscience Publishers, New York, London, 75-79.
-
6SIMONS J. Minimal varieties in riemannian manifolds [J]. J. Math. Soc. Japan, 1966, 18: 380-385.
-
7XIN Y L. Some results on stable harmonic maps [J]. Duke Math. J. , 1980, 47: 609-613.
-
8XIN Y L. Topology of certain submanifold in the Euclidean sphere [J]. Proc. Math. Soc., 1981, 84(4): 643-648.
-
9LEUNG P F. On the Stability of Harmonic Maps [M]. Lecture Notes math. , Springer Verlag, 1982,194: 122-129.
-
10LEUNG P F. A note on stable harmonic maps [J]. J. London Math. Soc. , 1984, 29:380-384
二级参考文献7
-
1吴传喜,1988年
-
2Pan Y L,Proc Amer Math Soc,1985年,93卷,111页
-
3Chen B Y,Total mean curvature and submanifolds of finite group,1984年
-
4Pan Y L,Chin Ann Math B,1982年,3卷,515页
-
5Xin Y L,Proc Amer Math Soc,1981年,82卷,643页
-
6Xin Y L,Duke Math J,1980年,47卷,609页
-
7Tai S S,J Diff Geom,1968年,2卷,55页
同被引文献6
-
1莫小欢.常曲率空间中具有平行平均曲率向量的子流形[J].数学年刊:A辑,1988,9(5):530-540.
-
2COLLINS G P. Computing with quantum knots[ J], Scientific American, 2006, 294 (4) : 56 - 63.
-
3BOURGUIGONON J P, LAWSON H B. Stability and isolation phemomena for Yang-Mills fields [ J ]. Commun Math Phys, 1981,79 : 189 - 230.
-
4KOBAYASHI S, OHINTA Y ,TAKUECHI M. On instability of Yang-Mills connections[J]. Math Z, 1986, 193:165 -189.
-
5SHEN C L. Weakly stability of Yang-Mills fields over the submanifolds of the sphere[ J]. Arch Math, 1982, 39:78 - 84.
-
6LIP. On the sobolev constant and the p-spectrum of a compact Riemannian manifold [ J ]. Ann Sci Norm Sup, 1980, 13:451-467.
-
1李亮.仅有2个不同主曲率的球面子流形[J].合肥工业大学学报(自然科学版),2009,32(5):749-753.
-
2沈学文,丁舜扬,徐慧群.De Sitter空间中的Yang-Mills场[J].哈尔滨工业大学学报,2008,40(3):502-504.
-
3孙弘安.球面子流形的内蕴刚性定理[J].南方冶金学院学报,1997,18(3):234-238.
-
4徐兆棣.局部对称共形平坦黎曼流形中的紧致子流形[J].Journal of Mathematical Research and Exposition,1996,16(1):76-80. 被引量:10
-
5李良树,周振荣.靶流形为球面子流形的调和映射的量子化现象(英文)[J].数学杂志,2012,32(3):423-430.
-
6鲍炎红.球面子流形的球面定理[J].安徽大学学报(自然科学版),2007,31(6):1-5.
-
7孔淑兰,方培德.球面子流形的整体内在刚性定理[J].贵州师范大学学报(自然科学版),1997,15(1):77-83.
-
8贺妍,张维维,李莎澜,刘清国.球面中具有平行平均曲率的子流形[J].空军雷达学院学报,2008,22(4):290-292.
-
9方培德,潮小李.球面子流形的几个整体Pinching定理[J].曲阜师范大学学报(自然科学版),1994,20(S1):43-46.
-
10吴炳烨.欧氏空间中具有常典则支撑函数的子流形[J].Journal of Mathematical Research and Exposition,1994,14(3):477-478.