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| On Energy Gap Phenomena of the Whitney Spheres in Cn or CPn* |
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Citation： |
Yong LUO,Liuyang ZHANG.On Energy Gap Phenomena of the Whitney Spheres in Cn or CPn*[J].Chinese Annals of Mathematics B,2023,44(4):599~614 |
| Page view： 1282
Net amount： 1744 |
Authors： |
Yong LUO; Liuyang ZHANG |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 12271069), the Natural Science Foundation of Chongqing (No. cstc2021jcyj-msxmX0443), the Chongqing “Zhitongche” foundation for doctors (No. CSTB2022BSXM-JCX0101) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJQN202201138). |
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| Abstract： |
Zhang (2021), Luo and Yin (2022) initiated the study of Lagrangian submanifolds satisfying ?*T = 0 or ?*?*T = 0 in Cn or CPn, where T = ?*h and h is the Lagrangian trace-free second fundamental form. They proved several rigidity theorems for Lagrangian surfaces satisfying ?*T = 0 or ?*?*T = 0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2. In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n ≥ 3 and to Lagrangian submanifolds in CPn. |
Keywords： |
Lagrangian submanifolds, Whitney spheres, Gap theorem, Conformal maslov form |
Classification： |
53C24, 53C42 |
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