| On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5） |
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| 引用本文： | Xiao Xiang,JIAO. On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）[J]. 数学学报(英文版), 2010, 26(4): 759-762. DOI: 10.1007/s10114-010-7262-0 |
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| 作者姓名： | Xiao Xiang JIAO |
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| 作者单位： | Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing 100049, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant No. 10531090）, Knowledge Innovation Funds of CAS （KJCX3-SYW-S03）, SRF for ROCS, SEM and the President Fund of GUCAS |
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| 摘 要： | Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.
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| 关 键 词： | 全纯曲线 Grassmann流形 格拉斯 常高斯曲率 非退化 证明 钾 |
On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2, 5) |
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| Xiao Xiang Jiao. On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2, 5)[J]. Acta Mathematica Sinica(English Series), 2010, 26(4): 759-762. DOI: 10.1007/s10114-010-7262-0 |
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| Authors: | Xiao Xiang Jiao |
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| Affiliation: | 1. Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
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| Abstract: | Let s: S 2 → G(2, 5) be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G(2, 5). It is prove that K is either 1/2 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/2 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or 4/3 if s is a non-degenerate holomorphic curve under some conditions. |
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| Keywords: | pseudo-holomorphic curves Gaussian curvature harmonic seouence. Kaihler angle |
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