An energy gap phenomenon for the Whitney sphere

Abstract

For an immersed Lagrangian submanifold, let $\check{A}$ be the Lagrangian trace-free second fundamental form. In this note we consider the equation ${\nabla }^{\ast }T=0$ on Lagrangian surfaces immersed in ${\mathbb{C}}^2$, where $T=-2{\nabla }^{\ast }(\check{A}┘\omega )$, and we prove a gap theorem for the Whitney sphere as a solution to this equation.

MZ-2019-595