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中国科学院大学学报 ›› 2011, Vol. 28 ›› Issue (2): 131-140.DOI: 10.7523/j.issn.2095-6134.2011.2.001

• 论文 •    下一篇

复格拉斯曼流形G(2,5)中的全纯2球

费杰, 焦晓祥   

  1. 中国科学院研究生院数学科学学院, 北京 100049
  • 收稿日期:2010-06-21 修回日期:2010-07-14 发布日期:2011-03-15
  • 基金资助:

    Supported by the NSFC (11071248), and the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-SO3)

Holomorphic 2-spheres in a complex Grassmann manifold G(2,5)

FEI Jie, JIAO Xiao-Xiang   

  1. School of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2010-06-21 Revised:2010-07-14 Published:2011-03-15
  • Supported by:

    Supported by the NSFC (11071248), and the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-SO3)

摘要:

利用调和序列和活动标架研究了复格拉斯曼流形G(2,5)中线性满的全纯2球.利用SU(2)的不可约酉表示构造了G(2,5)中的一些齐性全纯2球.在U(5)等价意义下确定常高斯曲率为2/3和4/3的所有线性满的退化全纯2球.最后证明在某一特定条件下常高斯曲率为4/3的非退化的全纯2球一定是U(5)等价的.

关键词: 全纯2球, 高斯曲率, 复格拉斯曼流形, 调和序列

Abstract:

We study the linearly full holomorphic 2-spheres in a complex Grassmann manifold G(2, 5) by using harmonic sequence and moving frames. We construct some examples of homogeneous holomorphic 2-spheres in G(2, 5) by applying the irreducible unitary representations of SU(2). Then, we determine all linearly full degenerate holomorphic 2-spheres with constant Gaussian curvatures of 2/3 and 4/3, up to U(5) equivalence. Moreover, we prove that all non-degenerate holomorphic 2-spheres with constant Gaussian curvature of 4/3 must be U(5) equivalent under some conditions.

Key words: holomorphic 2-sphere, Gaussian curvature, complex Grassmann manifold, harmonic sequence

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