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›› 2011, Vol. 28 ›› Issue (5): 573-582.DOI: 10.7523/j.issn.2095-6134.2011.5.002

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Harmonic two-spheres in the complex Grassmann manifold G(2,5)

LI Kang, JIAO Xiao-Xiang   

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2010-10-18 Revised:2010-12-08 Online:2011-09-15

Abstract:

We use the methods of harmonic sequences and moving frames to study the harmonic two-spheres in the complex Grassmann manifold G(2,5). Through the construction of holomorphic differential forms on S2, we can simplify the moving frames along a harmonic two-sphere in G(2,5). Finally, we give some upper bounds of the Gauss curvature of minimal two-spheres in G(2,5).

Key words: harmonic two-sphere, Gaussian curvature, holomorphic differential forms, harmonic sequence

CLC Number: