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| LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS |
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Citation： |
XIA Qiaoling,SHEN Yibing.LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS[J].Chinese Annals of Mathematics B,2005,26(3):347~360 |
| Page view： 1231
Net amount： 936 |
Authors： |
XIA Qiaoling; SHEN Yibing |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271106) and the Education Commission of Zhejiang Province of China (No.20030342). |
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| Abstract： |
The Ribaucour transformations for flat Lagrangian submanifolds in $C^n$ and $CP^n$ 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. |
Keywords： |
Lagrangian submanifold, Loop group action, Darboux transformation, Ribaucour transformation, Permutability formula |
Classification： |
53C25, 53C42, 58E40 |
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