Journal of University of Chinese Academy of Sciences >
Holomorphic 2-spheres in a complex Grassmann manifold G(2,5)
Received date: 2010-06-21
Revised date: 2010-07-14
Online 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)
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.
FEI Jie , JIAO Xiao-Xiang . Holomorphic 2-spheres in a complex Grassmann manifold G(2,5)[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(2) : 131 -140 . DOI: 10.7523/j.issn.2095-6134.2011.2.001
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