On energy gap phenomena of the Whitney sphere and related problems

We study Lagrangian submanifolds satisfying $\nabla^{*} T = 0$ introduced by Zhang (2021) in the complex space forms $N (4 c)$ ( $c = 0$ or $1$ ), where $T = \nabla^{*} \tilde{h}$ 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 $ℂ^{n}$ satisfying $\nabla^{*} \nabla^{*} T = 0$ and introduce a flow method related to them.

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Keywords

Lagrangian submanifolds, the Whitney sphere, energy gap theorems, conformal Maslov form

Mathematical Subject Classification

Primary: 53C24, 53C42

Milestones

Received: 25 August 2021

Revised: 13 June 2022

Accepted: 16 August 2022

Published: 15 February 2023

Authors

Yong Luo
Mathematical Science Research Center Chongqing University of Technology Chongqing China

Jiabin Yin
School of Mathematics and Statistics Guangxi Normal University Guilin China

Vol. 320, No. 2, 2022

Yong Luo and Jiabin Yin

Abstract

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Keywords

Mathematical Subject Classification

Milestones

Authors