| LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS |
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| 作者姓名： | XIA Qiaoling SHEN Yibing |
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| 作者单位： | XIA QIAOLING SHEN YIBING Department of Mathematics，Zhejiang University，Hangzhou 310027，China. Department of Mathematics，Zhejiang University，Hangzhou 310028，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10271106)
the Education Commission of Zhejiang Province of China (No.20030342). |
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| 摘 要： | The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.
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| 关 键 词： | 拉格朗日子流形 环群酌量 Darboux变换 Ribaucour变换 微分几何 |
| 收稿时间： | 3/4/2022 12:00:00 AM |
| 修稿时间： | 9/4/2016 12:00:00 AM |
LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS |
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| XIA Qiaoling,SHEN Yibing.LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS[J].Chinese Annals of Mathematics,Series B,2005,26(3):347-360. |
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| Authors: | XIA Qiaoling and SHEN Yibing |
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| Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2. Department of Mathematics, Zhejiang University, Hangzhou 310028, China |
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| Abstract: | The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula. |
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| Keywords: | Lagrangian submanifold Loop group action Darboux transformation Ribaucour transformation Permutability formula |
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