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arXiv 2006.081912020-06math.DG

On energy gap phenomena of the Whitney sphere and related problems

Yong Luo, Jiabin Yin

备注：: 18 pages, introduction rearranged and errors corrected.In the last version, we uplodaded a wrong file
发表信息：: Pacific J. Math. 320 (2022) 299-318
DOI：: 10.2140/pjm.2022.320.299

英文摘要：

In this paper, we study Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ introduced by Zhang \cite{Zh} in the complex space forms $N(4c)(c=0\ or \ 1)$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$ is the Lagrangian trace-free second fundamental form. We obtain some Simons' type integral inequalities and rigidity theorems for such Lagrangian submanifolds. Moreover we study Lagrangian submanifolds in $\mathbb{C}^n$ satisfying $\nabla^*\nabla^*T=0$ and introduce a flow method related to them.

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