Opers on transversely holomorphic foliations

Abstract

For real codimension two smooth foliations, we study the transversely complex structures, transversely complex projective structures and transverse opers associated to the foliation. We prove a uniqueness theorem for the transversely holomorphic $\mathbb{C}{\mathbb{P}}^1$--bundle naturally associated with a transversely complex projective structures. A similar uniqueness theorem is proved for the transversely holomorphic filtered $\mathbb{C}{\mathbb{P}}^{r-1}$--bundle naturally associated to a transverse $\mathrm{PGL}(r,\mathbb{C})$--oper.