2021/08/22 by Luo, Yong, Zhang, Liuyang
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.09657
In \citeZh \citeLY Zhang, Luo and Yin initiated the study of Lagrangian submanifolds satisfying \rm ∇^* T=0 or \rm ∇^*∇^*T=0 in ℂn or \mathbbCPn, where T =\rm ∇^*h and h is the Lagrangian trace-free second fundamental form. They proved several rigidity theorems for Lagrangian surfaces satisfying \rm ∇^* T=0 or \rm ∇^*∇^*T=0 in ℂ2 under proper small energy assumption and gave new characterization of the Whitney spheres in ℂ2. In this paper we extend these results to Lagrangian submanifolds in ℂn of dimension n≥3 and to Lagrangian submanifolds in \mathbbCPn.