Definition:Anti-Self-Dual 2-Form

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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.


Sources