Definition:Anti-Self-Dual 2-Form

Definition
Let $M$ be a $4$-dimensional oriented Riemannian manifold.

Let $\omega$ be a $2$-form on $M$.

Let $*$ be the Hodge star operator.

Suppose:


 * $* \omega = -\omega$

Then $\omega$ is known as the anti-self-dual $2$-form.