| 复格拉斯曼流形G(2,5)中的全纯2球 |
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| 作者姓名： | 费杰 焦晓祥 |
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| 作者单位： | 中国科学院研究生院数学科学学院, 北京 100049 |
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| 基金项目： | Supported by the NSFC (11071248), and the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-SO3) |
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| 摘 要： | 利用调和序列和活动标架研究了复格拉斯曼流形G(2,5)中线性满的全纯2球.利用SU(2)的不可约酉表示构造了G(2,5)中的一些齐性全纯2球.在U(5)等价意义下确定常高斯曲率为2/3和4/3的所有线性满的退化全纯2球.最后证明在某一特定条件下常高斯曲率为4/3的非退化的全纯2球一定是U(5)等价的.
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| 关 键 词： | 全纯2球 高斯曲率 复格拉斯曼流形 调和序列 |
| 收稿时间： | 2010-06-21 |
| 修稿时间： | 2010-07-14 |
Holomorphic 2-spheres in a complex Grassmann manifold G(2,5) |
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| Authors: | FEI Jie JIAO Xiao-Xiang |
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| Institution: | School of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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| 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. |
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| Keywords: | holomorphic 2-sphere Gaussian curvature complex Grassmann manifold harmonic sequence |
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