On torsion Kähler differential forms

Let k be a field of characteristic zero. Let V be an integral affine k-variety. We prove that any torsion Kähler differential form ω∈ΩV/k1(V) vanishes at every formal germ of curve on V. If V is an integral hypersurface of AkN (N≥1), we also prove that the non-cylindrical singular points of V belong to the singular locus of any torsion Kähler differential forms.