  If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form
which linearly deforms into contact forms, then M supports a K-contact form. On
the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if
and only if it is a fibration 1-form. on any other 2-torus bundle over the
circle, every closed, nonsingular 1-form deforms linearly into contact forms.
