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On energy gap phenomena of the Whitney sphere and related problems

Yong Luo and Jiabin Yin

Vol. 320 (2022), No. 2, 299–318
Abstract

We study Lagrangian submanifolds satisfying T = 0 introduced by Zhang (2021) in the complex space forms N(4c) (c = 0 or 1), where T = h~ and 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 n satisfying T = 0 and introduce a flow method related to them.

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