Minimal two-spheres with constant curvature in the complex Grassmannians

被引：0
作者：
Chiakuei Peng
Xiaowei Xu
机构：
[1] University of Chinese Academy of Sciences,School of Mathematical Sciences
[2] University of Science and Technology of China,School of Mathematical Sciences
[3] USTC Chinese Academy of Sciences,Wu Wen
来源：
Israel Journal of Mathematics | 2014年 / 202卷
关键词：
Fundamental Form; Constant Curvature; Minimal Immersion; Geodesic Submanifold; Cartan Form;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we use the Cartan embedding and the method of moving frames to study the geometry of 2-dimensional SU(2)-orbits in the complex Grassmann manifold G(k, n), and we express their geometric quantities explicitly. We obtain various minimal two-spheres in G(k, n) with constant curvature by studying the 2-dimensional orbits.
引用
收藏
页码：1 / 20
页数：19
相关论文
共 34 条
[1]  
Bando S.(1987) 2- Journal of the Mathematical Society of Japan 3 477-487
[2]  
Ohnita Y.(1988) ℂ Mathematische Annalen 279 599-620
[3]  
Bolton J.(1967) ℂ Journal of Differential Geometry 1 111-126
[4]  
Jensen G. R.(1983)Minimal immersions of surfaces in Euclidean spheres American Journal of Mathematics 105 59-83
[5]  
Rigoli M.(1987)Minimal surfaces by moving frames Annals of Mathematics 125 301-335
[6]  
Woodward L. M.(1989)Harmonic maps of the two-sphere into a complex Grassmann manifold II Transactions of the American Mathematical Society 313 393-406
[7]  
Calabi E.(2013)Rigidity of pseudo-holomorphic curves of constant curvature in Grassmann manifolds Journal of Geometry and Physics 66 24-33
[8]  
Chern S. S.(1980)Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions Nuclear Physics. B 174 397-406
[9]  
Wolfson J. G.(1971) ℂ Annals of Mathematics 93 43-62
[10]  
Chern S. S.(1983)Minimal immersions of spheres into spheres Advances in Mathematics 49 217-263
1234