The talk deals with holomorphic foliations admitting transversely holomorphic geometric structures. We will discuss a result of Ghys classifying codimension one holomorphic foliations on compact complex tori: those foliations are either linear or turbulent. We motivate and prove the following result: on the product of two elliptic curves, a generic nonsingular holomorphic turbulent foliation do not admit transversely complex projective structures. This is a joint work with Indranil Biswas (Shiv Nadar University).