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