| S~4到CP~n的常曲率弱Lagrangian极小浸入 |
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| 引用本文： | 黎镇琦,廖春艳.S~4到CP~n的常曲率弱Lagrangian极小浸入[J].数学学报,2012(2):369-384. |
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| 作者姓名： | 黎镇琦 廖春艳 |
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| 作者单位： | 南昌大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目(10671087);天元青年基金(11026109);江西省自然科学基金资助项目(2009GZS0017) |
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| 摘 要： | 研究球面S~4到CP~n的常曲率弱Lagrangian极小浸入■:S~4→CP~n.如果■的诱导度量ds~2具有常(截面)曲率c,则存在一个整数s≥1,使得c=4/s(s+3)].浸入■被两个四元齐次多项式f_s和f_(s-1)唯一确定.当s=1,即c=1,或s=2,即c=2/5时,浸入■是绝对实的.
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| 关 键 词： | 复射影空间 常曲率 弱Lagrangian极小浸入 |
Weakly Lagrangian Minimal Immersions of S~4 Into CP~n with Constant Curvature |
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| Zhen Qi LI Chun Yan LIAO.Weakly Lagrangian Minimal Immersions of S~4 Into CP~n with Constant Curvature[J].Acta Mathematica Sinica,2012(2):369-384. |
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| Authors: | Zhen Qi LI Chun Yan LIAO |
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| Institution: | Zhen Qi LI Chun Yan LIAO Department of Mathematics,Nanchang University,Nanchang 330031,P.R.China |
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| Abstract: | The weakly Lagrangian minimal immersions with constant curvature from S4 into CPn are studied.It is proved that if the induced metric has constant curvature c,than c = 4/s（s+ 3）]for some integer s≥1.And the immersionφ:S4→CPn is uniquely determined by two homogenous polynomials fs and fs-1 of four variables.If s = 1 or s = 2,or equivalently,if c = 1 or c = 2/5,the immersionφis absolute real. |
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| Keywords: | complex projective space constant curvature weakly Lagrangian minimal immersion |
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