Is there  a  singular  holomorphic foliation $F$ of  $\mathbb{C}P^2$ which  does not  admit  a global  transverse holomorphic  curve?  More  precisely there is no  an  immersed holomorphic submanifold  of  $\mathbb{C}P^2$  which intersect  all  regular  leaves, transversely? If there  exist  such  an  example $F$, does this  foliation admit  a smooth(but  not  necessarily holomorphic) global  transverse submanifold (of  real  dimension 2)?