Foliations on Projective Complete Intersection K3 Surfaces

We study foliations $\mathcal{F}$ on projective complete intersection K3 surfaces $X\hookrightarrow {\mathbb{P}}^n$, where $\mathcal{F}$ has isolated singularities and it is the restriction of a foliation of degree $d$ on ${\mathbb{P}}^n$ that leaves $X$ invariant. We compute the values of the degrees $d$ for which $\mathcal{F}$ is uniquely determined by its singular scheme.