An energy gap phenomenon for the Whitney sphere

Author:

Zhang Liuyang

Abstract

AbstractIn this paper, we study Lagrangian surfaces satisfying $$\nabla ^*T=0$$ T = 0 , where $$T=-2\nabla ^*(\check{A}\lrcorner \omega )$$ T = - 2 ( A ˇ ω ) and $$\check{A}$$ A ˇ is the Lagrangian trace-free second fundamental form. We obtain a gap lemma for such a Lagrangian surface.

Funder

Universitätsklinikum Freiburg

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference14 articles.

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5. Castro, I., Urbano, F.: Willmore surfaces of $$\mathbb{R}^4$$ and the Whitney Sphere. Ann. Glob. Anal. Geom. 19(2), 153–175 (2001)

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1. On Energy Gap Phenomena of the Whitney Spheres in ℂn or ℂℙn;Chinese Annals of Mathematics, Series B;2023-07

2. On energy gap phenomena of the Whitney sphere and related problems;Pacific Journal of Mathematics;2022-12-31

3. Gap theorems for Lagrangian submanifolds in complex space forms;Geometriae Dedicata;2021-09-18

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