A characterization of rationally convex immersions

Let S be a smooth, totally real, compact immersion in $\mathbb{C}^n$ of real dimension $m \leq n$, which is locally polynomially convex and it has finitely many points where it self-intersects finitely many times, transversely or non-transversely. Our result proves that S is rationally convex if and only if it is isotropic with respect to a ``degenerate" Kähler form in $\mathbb{C}^n$. We also show that  there exists a large class of such rationally convex immersions that are not isotropic with respect to any genuine (non-degenerate) Kähler form.