Foliations by curves on threefolds

We study the conormal sheaves and singular schemes of 1-dimensional foliations on smooth projective varieties $X$ dimension 3 Picard rank 1. prove that if scheme has 0, then sheaf is $\mu$-stable whenever tangent bundle $TX$ stable, apply this fact to characterization certain irreducible components moduli space 2 reflexive $\mathbb{P}^3$ a quadric hypersurface $Q_3\subset\mathbb{P}^4$. Finally, we give classification local complete intersection foliations, is, with locally free sheaves, degree 0 1 $Q_3$.