数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 237-248.doi: 10.1016/S0252-9602(11)60224-5

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ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)

焦晓祥|彭家贵   

  1. Department of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • 收稿日期:2008-04-22 修回日期:2009-02-27 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10531090), Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)

ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)

 JIAO Xiao-Xiang, PENG Jia-Gui   

  1. Department of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2008-04-22 Revised:2009-02-27 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (10531090), Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)

摘要:

In this article, it is proved that there doesn't exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2, 5) with constant curvature k=4/7, 1/2, 4/9. Thus, from [7] it follows that if φ: S2G(2, 5) is a nonsingular holomorphic curve with constant curvature K, then, K=4, 2, 4/3, 1 or  4/5.

关键词: Gauss curvature, holomorphic curve, complex Grassmann manifold

Abstract:

In this article, it is proved that there doesn't exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2, 5) with constant curvature k=4/7, 1/2, 4/9. Thus, from [7] it follows that if φ: S2G(2, 5) is a nonsingular holomorphic curve with constant curvature K, then, K=4, 2, 4/3, 1 or  4/5.

Key words: Gauss curvature, holomorphic curve, complex Grassmann manifold

中图分类号: 

  • 53C42