Acta mathematica scientia, Series B >
ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)
Received date: 2008-04-22
Revised date: 2009-02-27
Online published: 2011-01-20
Supported by
Supported by the National Natural Science Foundation of China (10531090), Knowledge Innovation Funds of CAS (KJCX3-SYW-S03)
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: S2→G(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
JIAO Xiao-Xiang , PENG Jia-Gui . ON HOLOMORPHIC CURVES OF CONSTANT CURVATURE IN THE COMPLEX GRASSMANN MANIFOLD G(2,5)[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 237 -248 . DOI: 10.1016/S0252-9602(11)60224-5
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