| 从S2到CPn 的共形极小浸入 |
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| 作者姓名： | 陈红霞 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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| 摘 要： | 通过李群、活动标架，以及调和映射来研究从S2到CPn的共形极小浸入．首先，用一种新方法证明Bolton的一个定理，从S2到的全纯曲线在差一个刚动的情况下由度量唯一决定；其次，利用从 S2到CPn的共形极小浸入来构造从S2到G2,n+1的共形极小浸入；最后，如果φ 是从S2到CPn 的全实共形极小浸入，且φ 是常曲率的，则可以找出具体的等距变换ｇ，使得ｇφ 包含在RPnCPn中．
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| 关 键 词： | 全纯曲线 极小浸入 调和映射 Gauss曲率 |
Conformal minimal immersions of S2 in CPn |
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| Authors: | Chen hong-xia Jiao xiao-xiang |
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| Institution: | Department of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | In this paper, conformal minimal 2-sphere immersed in a complex projective space are studied by applying Lie theory, moving frame and harmonic sequence. First, we use a different way from Bolton to prove that a holomorphic curve from S2 into CPn is uniquely determined by its induced metric, up to a rigid motion. Secondly, via conformal minimal immersions of constant curvature from S2 into CPn, we can construct new minimal immersions of S2 in G2,n+1 with constant curvature. Finally, if φ is a totally real conformal minimal 2-sphere of constant curvature immersed in a complex projective space, then we can find the explicit isometry transform ｇ such that ｇφ lies in RPn CPn. |
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| Keywords: | holomorphic curve minimal immersion harmonic sequence Gauss curvature |
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