On Energy Gap Phenomena of the Whitney Spheres in Cn or(C)(P)n

• Published in: 数学年刊B辑（英文版） Vol. 44; no. 4; pp. 599 - 614
• Main Authors: Yong LUO, Liuyang ZHANG
• Format: Journal Article
• Language: English
• Published: Mathematical Science Research Center,Chongqing University of Technology,Chongqing 400054,China 2023
• Subjects: Whitney spheres; Gap theorem; Lagrangian submanifolds; Conformal maslov form
• ISSN: 0252-9599
• DOI: 10.1007/s11401-023-0034-9

Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian subman-ifolds satisfying ▽*T=0 or ▽*▽*T=0 in(C)n or(C)(P)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 V*▽*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(C)n of dimension n≥3 and to Lagrangian submanifolds in(C)(P)n.