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›› 2011, Vol. 28 ›› Issue (2): 131-140.DOI: 10.7523/j.issn.2095-6134.2011.2.001

• Research Articles •     Next Articles

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 Online:2011-03-15
  • Supported by:

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

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

CLC Number: