• Corpus ID: 219687442

On energy gap phenomena of the Whitney sphere and related problems

@article{Luo2020OnEG,
  title={On energy gap phenomena of the Whitney sphere and related problems},
  author={Yong Luo and Jiabin Yin},
  journal={arXiv: Differential Geometry},
  year={2020}
}
In this paper, we study Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ introduced by Zhang \cite{Zh} in the complex space forms $N(4c)(c\geq0)$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$ is the Lagrangian trace-free second fundamental form. We obtain some integral inequalities and rigidity theorems for such Lagrangian submanifolds. Moreover we study Lagrangian surfaces in $\mathbb{C}^2$ satisfying $\nabla^*\nabla^*T=0$ and introduce a flow method related to them. 

On energy gap phenomena of the Whitney spheres in $\mathbb{C}^n$ or $\mathbb{CP}^n$

In [29] [19] Zhang, Luo and Yin initiated the study of Lagrangian submanifolds satisfying ∇T = 0 or ∇∇T = 0 in C or CP, where T = ∇∗h̃ and h̃ is the Lagrangian trace-free second fundamental form.

Gap theorems for Lagrangian submanifolds in complex space forms

In this paper, we investigate the gap phenomena for complete Lagrangian submanifolds satisfying ∇∗T≡0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}

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