Smooth automorphism preserves the Kähler class?

Question

Let $S\subset \mathbb {CP^3}$ be a Kähler surface, $[\omega]$ be the Kähler class. Let $f:S\to S$ be a smooth orientation preserving automorphism (in the category of smooth manifolds, i.e. not has to be holomorphic). Is it true that $f^*[\omega]=[\omega]$?