摘要
Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),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.
基金
supported by the National Natural Science Foundation of China(No.12271069)
the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxm X0443)
the Chongqing“Zhitongche”foundation for doctors(No.CSTB2022BSXM-JCX0101)
the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJQN202201138)。