数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1889-1898.doi: 10.1016/S0252-9602(11)60368-8

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CONSTRUCTION OF HOMOGENEOUS MINIMAL 2-SPHERES IN COMPLEX GRASSMANNIANS

费杰|焦晓祥|许小卫   

  1. Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing 100049 China； Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2010-01-21 修回日期:2010-10-15 出版日期:2011-09-20 发布日期:2011-09-20
  • 基金资助:

    Project supported by the NSFC (11071248, 11071249); the third author supported by the Fundamental Research Funds for the Central Universities(USTC).

CONSTRUCTION OF HOMOGENEOUS MINIMAL 2-SPHERES IN COMPLEX GRASSMANNIANS

 FEI Jie, JIAO Xiao-Xiang, XU Xiao-Wei   

  1. Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing 100049 China； Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
  • Received:2010-01-21 Revised:2010-10-15 Online:2011-09-20 Published:2011-09-20
  • Supported by:

    Project supported by the NSFC (11071248, 11071249); the third author supported by the Fundamental Research Funds for the Central Universities(USTC).

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摘要：

In this paper, we construct a class of homogeneous minimal 2-spheres in com-plex Grassmann manifolds by applying the irreducible unitary representations of SU(2). Furthermore, we compute induced metrics, Gaussian curvatures, Kähler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G(2, n + 1) by making use of Veronese sequence.

关键词: homogeneous 2-sphere, Gaussian curvature, Kähler angle, Veronese se-quence, complex Grassmann manifold

Abstract:

In this paper, we construct a class of homogeneous minimal 2-spheres in com-plex Grassmann manifolds by applying the irreducible unitary representations of SU(2). Furthermore, we compute induced metrics, Gaussian curvatures, Kähler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G(2, n + 1) by making use of Veronese sequence.

Key words: homogeneous 2-sphere, Gaussian curvature, Kähler angle, Veronese se-quence, complex Grassmann manifold

中图分类号: 

  • 53C42
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